static void Main(string[] args)
{
DateTime timer = DateTime.Now;
//////////////// DATES //////////////////////////////////////////////
Calendar calendar = new TARGET();
Date todaysDate = new Date(15, Month.January, 2017);
Date settlementDate = new Date(todaysDate);
Settings.setEvaluationDate(todaysDate);
DayCounter dayCounter = new Actual365Fixed();
//////////////// MARKET //////////////////////////////////////////////
// Spot
double underlying = 4468.17;
Handle <Quote> underlyingH = new Handle <Quote>(new SimpleQuote(underlying));
// riskfree
double riskFreeRate = 0.035;
Handle <YieldTermStructure> flatTermStructure = new Handle <YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
// dividend
double dividendYield = 0.0;
double fixedDiv = 5.0;
Handle <YieldTermStructure> flatDividendTS = new Handle <YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
Handle <YieldTermStructure> FixedDivTermStructure = new Handle <YieldTermStructure>(new FixedForward(settlementDate, fixedDiv, underlying, dayCounter));
// vol surface
Date StartDateVol = settlementDate + new Period(1, TimeUnit.Months);
List <int> maturityInDays = new InitializedList <int>()
{
0, 13, 41, 90, 165, 256, 345, 524, 703
};
List <Date> datesVol = new InitializedList <Date>();
for (int d = 1; d < maturityInDays.Count; d++)
{
datesVol.Add(calendar.advance(settlementDate, new Period(maturityInDays[d], TimeUnit.Days)));
}
List <double> strikes = new InitializedList <double>()
{
3400, 3600, 3800, 4000, 4200, 4400, 4500, 4600, 4800, 5000, 5200, 5400, 5600
};
Matrix blackVolMatrix = new Matrix(maturityInDays.Count - 1, strikes.Count, 0.2);
var vols = new InitializedList <double>()
{
0.6625, 0.4875, 0.4204, 0.3667, 0.3431, 0.3267, 0.3121, 0.3121,
0.6007, 0.4543, 0.3967, 0.3511, 0.3279, 0.3154, 0.2984, 0.2921,
0.5084, 0.4221, 0.3718, 0.3327, 0.3155, 0.3027, 0.2919, 0.2889,
0.4541, 0.3869, 0.3492, 0.3149, 0.2963, 0.2926, 0.2819, 0.2800,
0.4060, 0.3607, 0.3330, 0.2999, 0.2887, 0.2811, 0.2751, 0.2775,
0.3726, 0.3396, 0.3108, 0.2781, 0.2788, 0.2722, 0.2661, 0.2686,
0.3550, 0.3277, 0.3012, 0.2781, 0.2781, 0.2661, 0.2661, 0.2681,
0.3428, 0.3209, 0.2958, 0.2740, 0.2688, 0.2627, 0.2580, 0.2620,
0.3302, 0.3062, 0.2799, 0.2631, 0.2573, 0.2533, 0.2504, 0.2544,
0.3343, 0.2959, 0.2705, 0.2540, 0.2504, 0.2464, 0.2448, 0.2462,
0.3460, 0.2845, 0.2624, 0.2463, 0.2425, 0.2385, 0.2373, 0.2422,
0.3857, 0.2860, 0.2578, 0.2399, 0.2357, 0.2327, 0.2312, 0.2351,
0.3976, 0.2860, 0.2607, 0.2356, 0.2297, 0.2268, 0.2241, 0.2320
};
for (int i = 0; i < vols.Count; i++)
{
int testraw = (int)(i % (datesVol.Count));
int testcol = (int)(i / (datesVol.Count));
blackVolMatrix[testraw, testcol] = vols[i];
}
BlackVarianceSurface mySurface = new BlackVarianceSurface(settlementDate, calendar, datesVol,
strikes, Matrix.transpose(blackVolMatrix), dayCounter);
Handle <BlackVolTermStructure> mySurfaceH = new Handle <BlackVolTermStructure>(mySurface);
//////////////// CALIBRATION //////////////////////////////////////////////
Period helperPeriod = new Period();
//helpers
List <CalibrationHelper> calibrationHelpers = new List <CalibrationHelper>();
for (int k = 0; k < strikes.Count; k++)
{
for (int d = 0; d < datesVol.Count; d++)
{
helperPeriod = new Period(datesVol[d] - settlementDate, TimeUnit.Days);
calibrationHelpers.Add(new HestonModelHelper(helperPeriod,
calendar,
underlying,
strikes[k],
new Handle <Quote>(new SimpleQuote(blackVolMatrix[d, k])),
flatTermStructure,
flatDividendTS,
CalibrationHelper.CalibrationErrorType.ImpliedVolError));
}
}
// starting data
double v0 = 0.1;
double kappa = 1.0;
double theta = 0.1;
double sigma = 0.5;
double rho = -0.5;
// model
HestonProcess hestonProcess = new HestonProcess(flatTermStructure,
flatDividendTS,
underlyingH,
v0, kappa, theta, sigma, rho);
HestonModel hestonmodel = new HestonModel(hestonProcess);
AnalyticHestonEngine analyticHestonEngine = new AnalyticHestonEngine(hestonmodel);
foreach (HestonModelHelper hmh in calibrationHelpers)
{
hmh.setPricingEngine(analyticHestonEngine);
}
// optimization
double tolerance = 1.0e-8;
LevenbergMarquardt optimizationmethod = new LevenbergMarquardt(tolerance, tolerance, tolerance);
hestonmodel.calibrate(calibrationHelpers, optimizationmethod, new EndCriteria(400, 40, tolerance, tolerance, tolerance));
double error = 0.0;
List <double> errorList = new InitializedList <double>();
//////////////// CALIBRATION RESULTS //////////////////////////////////////////////
Console.WriteLine("Calbration :");
Console.WriteLine("-----------");
foreach (HestonModelHelper hmh in calibrationHelpers)
{
error += Math.Abs(hmh.calibrationError());
errorList.Add(Math.Abs(hmh.calibrationError()));
}
Vector hestonParameters = hestonmodel.parameters();
Console.WriteLine("v0 = {0:0.00%}", hestonParameters[4]);
Console.WriteLine("kappa = {0:0.00%}", hestonParameters[1]);
Console.WriteLine("theta = {0:0.00%}", hestonParameters[0]);
Console.WriteLine("sigma = {0:0.00%}", hestonParameters[2]);
Console.WriteLine("rho = {0:0.00%}", hestonParameters[3]);
Console.WriteLine();
Console.WriteLine("Total error = {0:0.0000}", error);
Console.WriteLine("Mean error = {0:0.0000%}", error / (errorList.Count - 1));
Console.WriteLine();
int StepsPerYear = 52;
double absoluteTolerance = 80.0;
ulong mcSeed = 42;
// MC Heston process
HestonProcess calibratedHestonProcess = new HestonProcess(flatTermStructure,
flatDividendTS,
underlyingH,
hestonParameters[4],
hestonParameters[1],
hestonParameters[0],
hestonParameters[2],
hestonParameters[3]);
// BS process
GeneralizedBlackScholesProcessTolerance bsmProcess = new GeneralizedBlackScholesProcessTolerance(underlyingH, FixedDivTermStructure, flatTermStructure, mySurfaceH);
//////////////// ENGINES /////////////////////////////////////////////////
IPricingEngine mcHestonEngine = new MakeMCEuropeanHestonEngine <PseudoRandom, Statistics>(calibratedHestonProcess)
.withStepsPerYear(StepsPerYear)
.withAbsoluteTolerance(absoluteTolerance)
.withSeed(mcSeed)
.getAsPricingEngine();
double absoluteTolerance2 = 1.0;
IPricingEngine mcGenHestonEngineTestbs = new MakeMCGenericScriptInstrument <PseudoRandom>(bsmProcess)
.withStepsPerYear(StepsPerYear)
.withAbsoluteTolerance(absoluteTolerance2)
.withSeed(mcSeed)
.value();
IPricingEngine mcGenHestonEngineTestbs2 = new MakeMCGenericScriptInstrument <PseudoRandom>(calibratedHestonProcess)
.withStepsPerYear(StepsPerYear)
.withAbsoluteTolerance(absoluteTolerance2)
.withSeed(mcSeed)
.value();
//////////////// PRICING //////////////////////////////////////////////
Console.WriteLine("Pricing Vanilla:");
Console.WriteLine("---------------");
Date maturity = new Date(17, Month.May, 2019);
Exercise europeanExercise = new EuropeanExercise(maturity);
Option.Type type = Option.Type.Call;
double strike = underlying;
StrikedTypePayoff payoff = new PlainVanillaPayoff(type, strike);
VanillaOption europeanOption = new VanillaOption(payoff, europeanExercise);
// heston
europeanOption.setPricingEngine(analyticHestonEngine);
Console.Write("Heston pricing = {0:0.0000}", europeanOption.NPV());
Console.WriteLine(" -> {0:0.0000%}", europeanOption.NPV() / underlying);
// Mc heston
europeanOption.setPricingEngine(mcHestonEngine);
Console.Write("HestMC pricing = {0:0.0000}", europeanOption.NPV());
Console.Write(" -> {0:0.0000%}", europeanOption.NPV() / underlying);
Console.WriteLine(" tolerance {0:0.0} / {1:0.00%}", absoluteTolerance, absoluteTolerance / underlying);
// analytic bs
europeanOption.setPricingEngine(new AnalyticEuropeanEngine(bsmProcess));
Console.Write("BS pricing = {0:0.0000}", europeanOption.NPV());
Console.WriteLine(" -> {0:0.0000%}", europeanOption.NPV() / underlying);
Console.WriteLine();
//////////////// AUTOCALL HESTON //////////////////////////////////////////////
List <Date> fixingdates = new InitializedList <Date>();
double coupon = 0.05;
double barrierlvl = 0.6;
for (int i = 1; i <= 4; i++)
{
fixingdates.Add(settlementDate + new Period(i, TimeUnit.Years));
}
ScriptGenericAutocall myGenericAutocallHTTEst = new ScriptGenericAutocall(fixingdates, coupon, barrierlvl, underlying);
myGenericAutocallHTTEst.setPricingEngine(mcGenHestonEngineTestbs);
Console.WriteLine("Pricing Autocall BS :");
Console.WriteLine("---------------------");
Console.WriteLine("test = {0:0.0000}", myGenericAutocallHTTEst.NPV());
Console.WriteLine("Err = {0:0.0000%}", myGenericAutocallHTTEst.errorEstimate() / myGenericAutocallHTTEst.NPV());
Console.WriteLine("Samples = {0}", myGenericAutocallHTTEst.samples());
Console.Write("\n");
for (int i = 0; i < 4; i++)
{
Console.WriteLine("ProbaCall {1} = {0:0.0000%}", myGenericAutocallHTTEst.inspout("ProbaCall " + i), i + 1);
}
Console.WriteLine("ProbaMid = {0:0.0000%}", myGenericAutocallHTTEst.inspout("ProbaMid"));
Console.WriteLine("probaDown = {0:0.0000%}", myGenericAutocallHTTEst.inspout("ProbaDown"));
Console.WriteLine("test = {0:0.0000%}", myGenericAutocallHTTEst.inspout("ProbaDown"));
Console.WriteLine("AvgDown/Proba = {0:0.0000%}", myGenericAutocallHTTEst.inspout("AvgDown") / myGenericAutocallHTTEst.inspout("ProbaDown"));
Console.Write("\n");
myGenericAutocallHTTEst.setPricingEngine(mcGenHestonEngineTestbs2);
Console.WriteLine("Pricing Autocall Heston:");
Console.WriteLine("------------------------");
Console.WriteLine("test = {0:0.0000}", myGenericAutocallHTTEst.NPV());
Console.WriteLine("Err = {0:0.0000%}", myGenericAutocallHTTEst.errorEstimate() / myGenericAutocallHTTEst.NPV());
Console.WriteLine("Samples = {0}", myGenericAutocallHTTEst.samples());
Console.Write("\n");
for (int i = 0; i < 4; i++)
{
Console.WriteLine("ProbaCall {1} = {0:0.0000%}", myGenericAutocallHTTEst.inspout("ProbaCall " + i), i + 1);
}
Console.WriteLine("ProbaMid = {0:0.0000%}", myGenericAutocallHTTEst.inspout("ProbaMid"));
Console.WriteLine("probaDown = {0:0.0000%}", myGenericAutocallHTTEst.inspout("ProbaDown"));
Console.WriteLine("test = {0:0.0000%}", myGenericAutocallHTTEst.inspout("ProbaDown"));
Console.WriteLine("AvgDown/Proba = {0:0.0000%}", myGenericAutocallHTTEst.inspout("AvgDown") / myGenericAutocallHTTEst.inspout("ProbaDown"));
Console.Write("\n");
//////////////// END TEST //////////////////////////////////////////////
Console.WriteLine();
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
static void Main(string[] args)
{
DateTime startTime = DateTime.Now;
Option.Type optionType = Option.Type.Put;
double underlyingPrice = 36;
double strikePrice = 40;
double dividendYield = 0.0;
double riskFreeRate = 0.06;
double volatility = 0.2;
Date todaysDate = new Date(15, Month.May, 1998);
Settings.instance().setEvaluationDate(todaysDate);
Date settlementDate = new Date(17, Month.May, 1998);
Date maturityDate = new Date(17, Month.May, 1999);
Calendar calendar = new TARGET();
DateVector exerciseDates = new DateVector(4);
for (int i = 1; i <= 4; i++)
{
Period forwardPeriod = new Period(3 * i, TimeUnit.Months);
Date forwardDate = settlementDate.Add(forwardPeriod);
exerciseDates.Add(forwardDate);
}
EuropeanExercise europeanExercise =
new EuropeanExercise(maturityDate);
BermudanExercise bermudanExercise =
new BermudanExercise(exerciseDates);
AmericanExercise americanExercise =
new AmericanExercise(settlementDate, maturityDate);
// bootstrap the yield/dividend/vol curves and create a
// BlackScholesMerton stochastic process
DayCounter dayCounter = new Actual365Fixed();
YieldTermStructureHandle flatRateTSH =
new YieldTermStructureHandle(
new FlatForward(settlementDate, riskFreeRate,
dayCounter));
YieldTermStructureHandle flatDividendTSH =
new YieldTermStructureHandle(
new FlatForward(settlementDate, dividendYield,
dayCounter));
BlackVolTermStructureHandle flatVolTSH =
new BlackVolTermStructureHandle(
new BlackConstantVol(settlementDate, calendar,
volatility, dayCounter));
QuoteHandle underlyingQuoteH =
new QuoteHandle(new SimpleQuote(underlyingPrice));
BlackScholesMertonProcess stochasticProcess =
new BlackScholesMertonProcess(underlyingQuoteH,
flatDividendTSH,
flatRateTSH,
flatVolTSH);
PlainVanillaPayoff payoff =
new PlainVanillaPayoff(optionType, strikePrice);
// options
VanillaOption europeanOption =
new VanillaOption(payoff, europeanExercise);
VanillaOption bermudanOption =
new VanillaOption(payoff, bermudanExercise);
VanillaOption americanOption =
new VanillaOption(payoff, americanExercise);
// report the parameters we are using
ReportParameters(optionType, underlyingPrice, strikePrice,
dividendYield, riskFreeRate,
volatility, maturityDate);
// write out the column headings
ReportHeadings();
#region Analytic Formulas
// Black-Scholes for European
try {
europeanOption.setPricingEngine(
new AnalyticEuropeanEngine(stochasticProcess));
ReportResults("Black-Scholes",
europeanOption.NPV(), null, null);
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Barone-Adesi and Whaley approximation for American
try {
americanOption.setPricingEngine(
new BaroneAdesiWhaleyEngine(stochasticProcess));
ReportResults("Barone-Adesi/Whaley",
null, null, americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Bjerksund and Stensland approximation for American
try {
americanOption.setPricingEngine(
new BjerksundStenslandEngine(stochasticProcess));
ReportResults("Bjerksund/Stensland",
null, null, americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Integral
try {
europeanOption.setPricingEngine(
new IntegralEngine(stochasticProcess));
ReportResults("Integral",
europeanOption.NPV(), null, null);
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
uint timeSteps = 801;
// Finite differences
try {
europeanOption.setPricingEngine(
new FDEuropeanEngine(stochasticProcess,
timeSteps, timeSteps - 1));
bermudanOption.setPricingEngine(
new FDBermudanEngine(stochasticProcess,
timeSteps, timeSteps - 1));
americanOption.setPricingEngine(
new FDAmericanEngine(stochasticProcess,
timeSteps, timeSteps - 1));
ReportResults("Finite differences",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
//Variance Gamma
try
{
VarianceGammaProcess vgProcess = new VarianceGammaProcess(underlyingQuoteH,
flatDividendTSH,
flatRateTSH,
volatility, 0.01, 0.0
);
europeanOption.setPricingEngine(
new VarianceGammaEngine(vgProcess));
ReportResults("Variance-Gamma",
europeanOption.NPV(), null, null);
}
catch (Exception e)
{
Console.WriteLine(e.ToString());
}
#endregion Analytic Formulas
#region Binomial Methods
// Binomial Jarrow-Rudd
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"jarrowrudd", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"jarrowrudd", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"jarrowrudd", timeSteps));
ReportResults("Binomial Jarrow-Rudd",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Cox-Ross-Rubinstein
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"coxrossrubinstein", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"coxrossrubinstein", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"coxrossrubinstein", timeSteps));
ReportResults("Binomial Cox-Ross-Rubinstein",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Additive Equiprobabilities
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"eqp", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"eqp", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"eqp", timeSteps));
ReportResults("Additive Equiprobabilities",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Trigeorgis
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"trigeorgis", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"trigeorgis", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"trigeorgis", timeSteps));
ReportResults("Binomial Trigeorgis",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Tian
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"tian", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"tian", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"tian", timeSteps));
ReportResults("Binomial Tian",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Leisen-Reimer
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"leisenreimer", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"leisenreimer", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"leisenreimer", timeSteps));
ReportResults("Binomial Leisen-Reimer",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Joshi
try {
europeanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"joshi4", timeSteps));
bermudanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"joshi4", timeSteps));
americanOption.setPricingEngine(
new BinomialVanillaEngine(stochasticProcess,
"joshi4", timeSteps));
ReportResults("Binomial Joshi",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
#endregion Binomial Methods
#region Monte Carlo Methods
// quantlib appears to use max numeric (int and real) values to test for 'null' (or rather 'default') values
// MC (crude)
try {
string traits = "pseudorandom";
int mcTimeSteps = 1;
int timeStepsPerYear = int.MaxValue;
bool brownianBridge = false;
bool antitheticVariate = false;
int requiredSamples = int.MaxValue;
double requiredTolerance = 0.02;
int maxSamples = int.MaxValue;
int seed = 42;
europeanOption.setPricingEngine(
new MCEuropeanEngine(stochasticProcess,
traits, mcTimeSteps,
timeStepsPerYear,
brownianBridge,
antitheticVariate,
requiredSamples,
requiredTolerance,
maxSamples, seed));
ReportResults("MC (crude)", europeanOption.NPV(), null, null);
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// MC (Sobol)
try {
string traits = "lowdiscrepancy";
int mcTimeSteps = 1;
int timeStepsPerYear = int.MaxValue;
bool brownianBridge = false;
bool antitheticVariate = false;
int requiredSamples = 32768; // 2^15
double requiredTolerance = double.MaxValue;
int maxSamples = int.MaxValue;
int seed = 0;
europeanOption.setPricingEngine(
new MCEuropeanEngine(stochasticProcess,
traits, mcTimeSteps,
timeStepsPerYear,
brownianBridge,
antitheticVariate,
requiredSamples,
requiredTolerance, maxSamples, seed));
ReportResults("MC (Sobol)", europeanOption.NPV(), null, null);
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// MC (Longstaff Schwartz)
/*
* try {
* // MCAmericanEngine is not currently exposed in SWIG
* //americanOption.setPricingEngine(new MCAmericanEngine());
* ReportResults("MC (Longstaff Schwartz)", null, null, null);
* }
* catch (Exception e) {
* Console.WriteLine(e.ToString());
* }
*/
#endregion Monte Carlo Methods
DateTime endTime = DateTime.Now;
TimeSpan delta = endTime - startTime;
Console.WriteLine();
Console.WriteLine("Run completed in {0} s", delta.TotalSeconds);
Console.WriteLine();
}
public void testMethodOfLinesAndCN()
{
//Testing method of lines to solve Heston PDEs...
using (SavedSettings backup = new SavedSettings())
{
DayCounter dc = new Actual365Fixed();
Date today = new Date(21, 2, 2018);
Settings.Instance.setEvaluationDate(today);
Handle <Quote> spot = new Handle <Quote>(new SimpleQuote(100.0));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.0, dc));
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.0, dc));
double v0 = 0.09;
double kappa = 1.0;
double theta = v0;
double sigma = 0.4;
double rho = -0.75;
Date maturity = today + new Period(3, TimeUnit.Months);
HestonModel model =
new HestonModel(
new HestonProcess(rTS, qTS, spot, v0, kappa, theta, sigma, rho));
int xGrid = 21;
int vGrid = 7;
IPricingEngine fdmDefault =
new FdHestonVanillaEngine(model, 10, xGrid, vGrid, 0);
IPricingEngine fdmMol =
new FdHestonVanillaEngine(
model, 10, xGrid, vGrid, 0, new FdmSchemeDesc().MethodOfLines());
PlainVanillaPayoff payoff =
new PlainVanillaPayoff(Option.Type.Put, spot.currentLink().value());
VanillaOption option = new VanillaOption(payoff, new AmericanExercise(maturity));
option.setPricingEngine(fdmMol);
double calculatedMoL = option.NPV();
option.setPricingEngine(fdmDefault);
double expected = option.NPV();
double tol = 0.005;
double diffMoL = Math.Abs(expected - calculatedMoL);
if (diffMoL > tol)
{
QAssert.Fail("Failed to reproduce european option values with MOL"
+ "\n calculated: " + calculatedMoL
+ "\n expected: " + expected
+ "\n difference: " + diffMoL
+ "\n tolerance: " + tol);
}
IPricingEngine fdmCN =
new FdHestonVanillaEngine(model, 10, xGrid, vGrid, 0, new FdmSchemeDesc().CrankNicolson());
option.setPricingEngine(fdmCN);
double calculatedCN = option.NPV();
double diffCN = Math.Abs(expected - calculatedCN);
if (diffCN > tol)
{
QAssert.Fail("Failed to reproduce european option values with Crank-Nicolson"
+ "\n calculated: " + calculatedCN
+ "\n expected: " + expected
+ "\n difference: " + diffCN
+ "\n tolerance: " + tol);
}
BarrierOption barrierOption =
new BarrierOption(Barrier.Type.DownOut, 85.0, 10.0,
payoff, new EuropeanExercise(maturity));
barrierOption.setPricingEngine(new FdHestonBarrierEngine(model, 100, 31, 11));
double expectedBarrier = barrierOption.NPV();
barrierOption.setPricingEngine(new FdHestonBarrierEngine(model, 100, 31, 11, 0, new FdmSchemeDesc().MethodOfLines()));
double calculatedBarrierMoL = barrierOption.NPV();
double barrierTol = 0.01;
double barrierDiffMoL = Math.Abs(expectedBarrier - calculatedBarrierMoL);
if (barrierDiffMoL > barrierTol)
{
QAssert.Fail("Failed to reproduce barrier option values with MOL"
+ "\n calculated: " + calculatedBarrierMoL
+ "\n expected: " + expectedBarrier
+ "\n difference: " + barrierDiffMoL
+ "\n tolerance: " + barrierTol);
}
barrierOption.setPricingEngine(new FdHestonBarrierEngine(model, 100, 31, 11, 0, new FdmSchemeDesc().CrankNicolson()));
double calculatedBarrierCN = barrierOption.NPV();
double barrierDiffCN = Math.Abs(expectedBarrier - calculatedBarrierCN);
if (barrierDiffCN > barrierTol)
{
QAssert.Fail("Failed to reproduce barrier option values with Crank-Nicolson"
+ "\n calculated: " + calculatedBarrierCN
+ "\n expected: " + expectedBarrier
+ "\n difference: " + barrierDiffCN
+ "\n tolerance: " + barrierTol);
}
}
}
public void testSpuriousOscillations()
{
//Testing for spurious oscillations when solving the Heston PDEs...
using (SavedSettings backup = new SavedSettings())
{
DayCounter dc = new Actual365Fixed();
Date today = new Date(7, 6, 2018);
Settings.Instance.setEvaluationDate(today);
Handle <Quote> spot = new Handle <Quote>(new SimpleQuote(100.0));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.1, dc));
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.0, dc));
double v0 = 0.005;
double kappa = 1.0;
double theta = 0.005;
double sigma = 0.4;
double rho = -0.75;
Date maturity = today + new Period(1, TimeUnit.Years);
HestonProcess process =
new HestonProcess(
rTS, qTS, spot, v0, kappa, theta, sigma, rho);
HestonModel model =
new HestonModel(process);
FdHestonVanillaEngine hestonEngine =
new FdHestonVanillaEngine(
model, 6, 200, 13, 0, new FdmSchemeDesc().TrBDF2());
VanillaOption option = new VanillaOption(new PlainVanillaPayoff(Option.Type.Call, spot.currentLink().value()),
new EuropeanExercise(maturity));
option.setupArguments(hestonEngine.getArguments());
List <Tuple <FdmSchemeDesc, string, bool> > descs = new List <Tuple <FdmSchemeDesc, string, bool> >();
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().CraigSneyd(), "Craig-Sneyd", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().Hundsdorfer(), "Hundsdorfer", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().ModifiedHundsdorfer(), "Mod. Hundsdorfer", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().Douglas(), "Douglas", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().CrankNicolson(), "Crank-Nicolson", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().ImplicitEuler(), "Implicit", false));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().TrBDF2(), "TR-BDF2", false));
for (int j = 0; j < descs.Count; ++j)
{
FdmHestonSolver solver =
new FdmHestonSolver(new Handle <HestonProcess>(process),
hestonEngine.getSolverDesc(1.0),
descs[j].Item1);
List <double> gammas = new List <double>();
for (double x = 99; x < 101.001; x += 0.1)
{
gammas.Add(solver.gammaAt(x, v0));
}
double maximum = Double.MinValue;
for (int i = 1; i < gammas.Count; ++i)
{
double diff = Math.Abs(gammas[i] - gammas[i - 1]);
if (diff > maximum)
{
maximum = diff;
}
}
double tol = 0.01;
bool hasSpuriousOscillations = maximum > tol;
if (hasSpuriousOscillations != descs[j].Item3)
{
QAssert.Fail("unable to reproduce spurious oscillation behaviour "
+ "\n scheme name : " + descs[j].Item2
+ "\n oscillations observed: "
+ hasSpuriousOscillations
+ "\n oscillations expected: " + descs[j].Item3
);
}
}
}
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(Actual365Fixed obj)
{
return((obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr);
}
static void Main(string[] args)
{
const int xSteps = 100;
const int tSteps = 25;
const int dampingSteps = 0;
Date today = new Date(15, Month.January, 2020);
Settings.instance().setEvaluationDate(today);
DayCounter dc = new Actual365Fixed();
YieldTermStructureHandle rTS = new YieldTermStructureHandle(
new FlatForward(today, 0.06, dc));
YieldTermStructureHandle qTS = new YieldTermStructureHandle(
new FlatForward(today, 0.02, dc));
const double strike = 110.0;
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, strike);
Date maturityDate = today.Add(new Period(1, TimeUnit.Years));
double maturity = dc.yearFraction(today, maturityDate);
Exercise exercise = new AmericanExercise(today, maturityDate);
Instrument vanillaOption = new VanillaOption(payoff, exercise);
QuoteHandle spot = new QuoteHandle(new SimpleQuote(100.0));
BlackVolTermStructureHandle volatility = new BlackVolTermStructureHandle(
new BlackConstantVol(today, new TARGET(), 0.20, dc));
BlackScholesMertonProcess process =
new BlackScholesMertonProcess(spot, qTS, rTS, volatility);
vanillaOption.setPricingEngine(new FdBlackScholesVanillaEngine(
process, tSteps, xSteps, dampingSteps));
double expected = vanillaOption.NPV();
// build an PDE engine from scratch
Fdm1dMesher equityMesher = new FdmBlackScholesMesher(
xSteps, process, maturity, strike,
nullDouble(), nullDouble(), 0.0001, 1.5,
new DoublePair(strike, 0.1));
FdmMesherComposite mesher = new FdmMesherComposite(equityMesher);
FdmLinearOpComposite op = new FdmBlackScholesOp(mesher, process, strike);
FdmInnerValueCalculator calc = new FdmLogInnerValue(payoff, mesher, 0);
QlArray x = new QlArray(equityMesher.size());
QlArray rhs = new QlArray(equityMesher.size());
FdmLinearOpIterator iter = mesher.layout().begin();
for (uint i = 0; i < rhs.size(); ++i, iter.increment())
{
x.set(i, mesher.location(iter, 0));
rhs.set(i, calc.avgInnerValue(iter, maturity));
}
FdmBoundaryConditionSet bcSet = new FdmBoundaryConditionSet();
FdmStepConditionComposite stepCondition =
FdmStepConditionComposite.vanillaComposite(
new DividendSchedule(), exercise, mesher, calc, today, dc);
FdmLinearOpComposite proxyOp = new FdmLinearOpCompositeProxy(
new FdmBSDelegate(op));
FdmBackwardSolver solver = new FdmBackwardSolver(
proxyOp, bcSet, stepCondition, FdmSchemeDesc.Douglas());
solver.rollback(rhs, maturity, 0.0, tSteps, dampingSteps);
double logS = Math.Log(spot.value());
double calculated = new CubicNaturalSpline(x, rhs).call(logS);
Console.WriteLine("Homebrew PDE engine : {0:0.0000}", calculated);
Console.WriteLine("FdBlackScholesVanillaEngine: {0:0.0000}", expected);
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
/*********************
*** MARKET DATA ***
*********************/
Calendar calendar = new TARGET();
Date settlementDate = new Date(18, Month.September, 2008);
// must be a business day
settlementDate = calendar.adjust(settlementDate);
int fixingDays = 3;
int settlementDays = 3;
Date todaysDate = calendar.advance(settlementDate, -fixingDays, TimeUnit.Days);
// nothing to do with Date::todaysDate
Settings.setEvaluationDate(todaysDate);
Console.WriteLine("Today: {0}, {1}", todaysDate.DayOfWeek, todaysDate);
Console.WriteLine("Settlement date: {0}, {1}", settlementDate.DayOfWeek, settlementDate);
// Building of the bonds discounting yield curve
/*********************
*** RATE HELPERS ***
*********************/
// RateHelpers are built from the above quotes together with
// other instrument dependant infos. Quotes are passed in
// relinkable handles which could be relinked to some other
// data source later.
// Common data
// ZC rates for the short end
double zc3mQuote=0.0096;
double zc6mQuote=0.0145;
double zc1yQuote=0.0194;
Quote zc3mRate = new SimpleQuote(zc3mQuote);
Quote zc6mRate = new SimpleQuote(zc6mQuote);
Quote zc1yRate = new SimpleQuote(zc1yQuote);
DayCounter zcBondsDayCounter = new Actual365Fixed();
RateHelper zc3m = new DepositRateHelper(new Handle<Quote>(zc3mRate),
new Period(3, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
RateHelper zc6m = new DepositRateHelper(new Handle<Quote>(zc6mRate),
new Period(6, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
RateHelper zc1y = new DepositRateHelper(new Handle<Quote>(zc1yRate),
new Period(1, TimeUnit.Years), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
// setup bonds
double redemption = 100.0;
const int numberOfBonds = 5;
Date[] issueDates = {
new Date (15, Month.March, 2005),
new Date (15, Month.June, 2005),
new Date (30, Month.June, 2006),
new Date (15, Month.November, 2002),
new Date (15, Month.May, 1987)
};
Date[] maturities = {
new Date (31, Month.August, 2010),
new Date (31, Month.August, 2011),
new Date (31, Month.August, 2013),
new Date (15, Month.August, 2018),
new Date (15, Month.May, 2038)
};
double[] couponRates = {
0.02375,
0.04625,
0.03125,
0.04000,
0.04500
};
double[] marketQuotes = {
100.390625,
106.21875,
100.59375,
101.6875,
102.140625
};
List<SimpleQuote> quote = new List<SimpleQuote>();
for (int i=0; i<numberOfBonds; i++) {
SimpleQuote cp = new SimpleQuote(marketQuotes[i]);
quote.Add(cp);
}
List<RelinkableHandle<Quote>> quoteHandle = new InitializedList<RelinkableHandle<Quote>>(numberOfBonds);
for (int i=0; i<numberOfBonds; i++) {
quoteHandle[i].linkTo(quote[i]);
}
// Definition of the rate helpers
List<FixedRateBondHelper> bondsHelpers = new List<FixedRateBondHelper>();
for (int i=0; i<numberOfBonds; i++) {
Schedule schedule = new Schedule(issueDates[i], maturities[i], new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted,
DateGeneration.Rule.Backward, false);
FixedRateBondHelper bondHelper = new FixedRateBondHelper(quoteHandle[i],
settlementDays,
100.0,
schedule,
new List<double>() { couponRates[i] },
new ActualActual(ActualActual.Convention.Bond),
BusinessDayConvention.Unadjusted,
redemption,
issueDates[i]);
bondsHelpers.Add(bondHelper);
}
/*********************
** CURVE BUILDING **
*********************/
// Any DayCounter would be fine.
// ActualActual::ISDA ensures that 30 years is 30.0
DayCounter termStructureDayCounter = new ActualActual(ActualActual.Convention.ISDA);
double tolerance = 1.0e-15;
// A depo-bond curve
List<RateHelper> bondInstruments = new List<RateHelper>();
// Adding the ZC bonds to the curve for the short end
bondInstruments.Add(zc3m);
bondInstruments.Add(zc6m);
bondInstruments.Add(zc1y);
// Adding the Fixed rate bonds to the curve for the long end
for (int i=0; i<numberOfBonds; i++) {
bondInstruments.Add(bondsHelpers[i]);
}
YieldTermStructure bondDiscountingTermStructure = new PiecewiseYieldCurve<Discount,LogLinear>(
settlementDate, bondInstruments,
termStructureDayCounter,
new List<Handle<Quote>>(),
new List<Date>(),
tolerance);
// Building of the Libor forecasting curve
// deposits
double d1wQuote=0.043375;
double d1mQuote=0.031875;
double d3mQuote=0.0320375;
double d6mQuote=0.03385;
double d9mQuote=0.0338125;
double d1yQuote=0.0335125;
// swaps
double s2yQuote=0.0295;
double s3yQuote=0.0323;
double s5yQuote=0.0359;
double s10yQuote=0.0412;
double s15yQuote=0.0433;
/********************
*** QUOTES ***
********************/
// SimpleQuote stores a value which can be manually changed;
// other Quote subclasses could read the value from a database
// or some kind of data feed.
// deposits
Quote d1wRate = new SimpleQuote(d1wQuote);
Quote d1mRate = new SimpleQuote(d1mQuote);
Quote d3mRate = new SimpleQuote(d3mQuote);
Quote d6mRate = new SimpleQuote(d6mQuote);
Quote d9mRate = new SimpleQuote(d9mQuote);
Quote d1yRate = new SimpleQuote(d1yQuote);
// swaps
Quote s2yRate = new SimpleQuote(s2yQuote);
Quote s3yRate = new SimpleQuote(s3yQuote);
Quote s5yRate = new SimpleQuote(s5yQuote);
Quote s10yRate = new SimpleQuote(s10yQuote);
Quote s15yRate = new SimpleQuote(s15yQuote);
/*********************
*** RATE HELPERS ***
*********************/
// RateHelpers are built from the above quotes together with
// other instrument dependant infos. Quotes are passed in
// relinkable handles which could be relinked to some other
// data source later.
// deposits
DayCounter depositDayCounter = new Actual360();
RateHelper d1w = new DepositRateHelper(
new Handle<Quote>(d1wRate),
new Period(1, TimeUnit.Weeks), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d1m = new DepositRateHelper(
new Handle<Quote>(d1mRate),
new Period(1, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d3m = new DepositRateHelper(
new Handle<Quote>(d3mRate),
new Period(3, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d6m = new DepositRateHelper(
new Handle<Quote>(d6mRate),
new Period(6, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d9m = new DepositRateHelper(
new Handle<Quote>(d9mRate),
new Period(9, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d1y = new DepositRateHelper(
new Handle<Quote>(d1yRate),
new Period(1, TimeUnit.Years), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
// setup swaps
Frequency swFixedLegFrequency =Frequency.Annual;
BusinessDayConvention swFixedLegConvention = BusinessDayConvention.Unadjusted;
DayCounter swFixedLegDayCounter = new Thirty360(Thirty360.Thirty360Convention.European);
IborIndex swFloatingLegIndex = new Euribor6M();
Period forwardStart = new Period(1, TimeUnit.Days);
RateHelper s2y = new SwapRateHelper(
new Handle<Quote>(s2yRate), new Period(2, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
RateHelper s3y = new SwapRateHelper(
new Handle<Quote>(s3yRate), new Period(3, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
RateHelper s5y = new SwapRateHelper(
new Handle<Quote>(s5yRate), new Period(5, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
RateHelper s10y = new SwapRateHelper(
new Handle<Quote>(s10yRate), new Period(10, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
RateHelper s15y = new SwapRateHelper(
new Handle<Quote>(s15yRate), new Period(15, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle<Quote>(),forwardStart);
/*********************
** CURVE BUILDING **
*********************/
// Any DayCounter would be fine.
// ActualActual::ISDA ensures that 30 years is 30.0
// A depo-swap curve
List<RateHelper> depoSwapInstruments = new List<RateHelper>();
depoSwapInstruments.Add(d1w);
depoSwapInstruments.Add(d1m);
depoSwapInstruments.Add(d3m);
depoSwapInstruments.Add(d6m);
depoSwapInstruments.Add(d9m);
depoSwapInstruments.Add(d1y);
depoSwapInstruments.Add(s2y);
depoSwapInstruments.Add(s3y);
depoSwapInstruments.Add(s5y);
depoSwapInstruments.Add(s10y);
depoSwapInstruments.Add(s15y);
YieldTermStructure depoSwapTermStructure = new PiecewiseYieldCurve<Discount,LogLinear>(
settlementDate, depoSwapInstruments,
termStructureDayCounter,
new List<Handle<Quote> >(),
new List<Date>(),
tolerance);
// Term structures that will be used for pricing:
// the one used for discounting cash flows
RelinkableHandle<YieldTermStructure> discountingTermStructure = new RelinkableHandle<YieldTermStructure>();
// the one used for forward rate forecasting
RelinkableHandle<YieldTermStructure> forecastingTermStructure = new RelinkableHandle<YieldTermStructure>();
/*********************
* BONDS TO BE PRICED *
**********************/
// Common data
double faceAmount = 100;
// Pricing engine
IPricingEngine bondEngine = new DiscountingBondEngine(discountingTermStructure);
// Zero coupon bond
ZeroCouponBond zeroCouponBond = new ZeroCouponBond(
settlementDays,
new UnitedStates(UnitedStates.Market.GovernmentBond),
faceAmount,
new Date(15, Month.August,2013),
BusinessDayConvention.Following,
116.92,
new Date(15, Month.August,2003));
zeroCouponBond.setPricingEngine(bondEngine);
// Fixed 4.5% US Treasury Note
Schedule fixedBondSchedule = new Schedule(new Date(15, Month.May, 2007),
new Date(15,Month.May,2017), new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, false);
FixedRateBond fixedRateBond = new FixedRateBond(
settlementDays,
faceAmount,
fixedBondSchedule,
new List<double>() { 0.045 },
new ActualActual(ActualActual.Convention.Bond),
BusinessDayConvention.ModifiedFollowing,
100.0, new Date(15, Month.May, 2007));
fixedRateBond.setPricingEngine(bondEngine);
// Floating rate bond (3M USD Libor + 0.1%)
// Should and will be priced on another curve later...
RelinkableHandle<YieldTermStructure> liborTermStructure = new RelinkableHandle<YieldTermStructure>();
IborIndex libor3m = new USDLibor(new Period(3, TimeUnit.Months), liborTermStructure);
libor3m.addFixing(new Date(17, Month.July, 2008),0.0278625);
Schedule floatingBondSchedule = new Schedule(new Date(21, Month.October, 2005),
new Date(21, Month.October, 2010), new Period(Frequency.Quarterly),
new UnitedStates(UnitedStates.Market.NYSE),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, true);
FloatingRateBond floatingRateBond = new FloatingRateBond(
settlementDays,
faceAmount,
floatingBondSchedule,
libor3m,
new Actual360(),
BusinessDayConvention.ModifiedFollowing,
2,
// Gearings
new List<double>() { 1.0 },
// Spreads
new List<double>() { 0.001 },
// Caps
new List<double>(),
// Floors
new List<double>(),
// Fixing in arrears
true,
100.0,
new Date(21, Month.October, 2005));
floatingRateBond.setPricingEngine(bondEngine);
// Coupon pricers
IborCouponPricer pricer = new BlackIborCouponPricer();
// optionLet volatilities
double volatility = 0.0;
Handle<OptionletVolatilityStructure> vol;
vol = new Handle<OptionletVolatilityStructure>(
new ConstantOptionletVolatility(
settlementDays,
calendar,
BusinessDayConvention.ModifiedFollowing,
volatility,
new Actual365Fixed()));
pricer.setCapletVolatility(vol);
Utils.setCouponPricer(floatingRateBond.cashflows(),pricer);
// Yield curve bootstrapping
forecastingTermStructure.linkTo(depoSwapTermStructure);
discountingTermStructure.linkTo(bondDiscountingTermStructure);
// We are using the depo & swap curve to estimate the future Libor rates
liborTermStructure.linkTo(depoSwapTermStructure);
/***************
* BOND PRICING *
****************/
// write column headings
int[] widths = { 18, 10, 10, 10 };
Console.WriteLine("{0,18}{1,10}{2,10}{3,10}", "", "ZC", "Fixed", "Floating");
string separator = " | ";
int width = widths[0]
+ widths[1]
+ widths[2]
+ widths[3];
string rule = "".PadLeft(width, '-'), dblrule = "".PadLeft(width, '=');
string tab = "".PadLeft(8, ' ');
Console.WriteLine(rule);
Console.WriteLine("Net present value".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.NPV(),
fixedRateBond.NPV(),
floatingRateBond.NPV());
Console.WriteLine("Clean price".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.cleanPrice(),
fixedRateBond.cleanPrice(),
floatingRateBond.cleanPrice());
Console.WriteLine("Dirty price".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.dirtyPrice(),
fixedRateBond.dirtyPrice(),
floatingRateBond.dirtyPrice());
Console.WriteLine("Accrued coupon".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.accruedAmount(),
fixedRateBond.accruedAmount(),
floatingRateBond.accruedAmount());
Console.WriteLine("Previous coupon".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
"N/A",
fixedRateBond.previousCoupon(),
floatingRateBond.previousCoupon());
Console.WriteLine("Next coupon".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
"N/A",
fixedRateBond.nextCoupon(),
floatingRateBond.nextCoupon());
Console.WriteLine("Yield".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
zeroCouponBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
fixedRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
floatingRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual));
Console.WriteLine();
// Other computations
Console.WriteLine("Sample indirect computations (for the floating rate bond): ");
Console.WriteLine(rule);
Console.WriteLine("Yield to Clean Price: {0:n2}",
floatingRateBond.cleanPrice(floatingRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
new Actual360(), Compounding.Compounded, Frequency.Annual,
settlementDate));
Console.WriteLine("Clean Price to Yield: {0:0.00%}",
floatingRateBond.yield(floatingRateBond.cleanPrice(),new Actual360(), Compounding.Compounded, Frequency.Annual,
settlementDate));
/* "Yield to Price"
"Price to Yield" */
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
public void consistency()
{
// check inflation leg vs calculation directly from inflation TS
CommonVars common = new CommonVars();
// ZeroInflationSwap aka CPISwap
CPISwap.Type type = CPISwap.Type.Payer;
double nominal = 1000000.0;
bool subtractInflationNominal = true;
// float+spread leg
double spread = 0.0;
DayCounter floatDayCount = new Actual365Fixed();
BusinessDayConvention floatPaymentConvention = BusinessDayConvention.ModifiedFollowing;
int fixingDays = 0;
IborIndex floatIndex = new GBPLibor(new Period(6, TimeUnit.Months), common.nominalUK);
// fixed x inflation leg
double fixedRate = 0.1; //1% would be 0.01
double baseCPI = 206.1; // would be 206.13871 if we were interpolating
DayCounter fixedDayCount = new Actual365Fixed();
BusinessDayConvention fixedPaymentConvention = BusinessDayConvention.ModifiedFollowing;
Calendar fixedPaymentCalendar = new UnitedKingdom();
ZeroInflationIndex fixedIndex = common.ii;
Period contractObservationLag = common.contractObservationLag;
InterpolationType observationInterpolation = common.contractObservationInterpolation;
// set the schedules
Date startDate = new Date(2, Month.October, 2007);
Date endDate = new Date(2, Month.October, 2052);
Schedule floatSchedule = new MakeSchedule().from(startDate).to(endDate)
.withTenor(new Period(6, TimeUnit.Months))
.withCalendar(new UnitedKingdom())
.withConvention(floatPaymentConvention)
.backwards().value();
Schedule fixedSchedule = new MakeSchedule().from(startDate).to(endDate)
.withTenor(new Period(6, TimeUnit.Months))
.withCalendar(new UnitedKingdom())
.withConvention(BusinessDayConvention.Unadjusted)
.backwards().value();
CPISwap zisV = new CPISwap(type, nominal, subtractInflationNominal,
spread, floatDayCount, floatSchedule,
floatPaymentConvention, fixingDays, floatIndex,
fixedRate, baseCPI, fixedDayCount, fixedSchedule,
fixedPaymentConvention, contractObservationLag,
fixedIndex, observationInterpolation);
Date asofDate = Settings.evaluationDate();
double[] floatFix = { 0.06255, 0.05975, 0.0637, 0.018425, 0.0073438, -1, -1 };
double[] cpiFix = { 211.4, 217.2, 211.4, 213.4, -2, -2 };
for (int i = 0; i < floatSchedule.Count; i++)
{
if (floatSchedule[i] < common.evaluationDate)
{
floatIndex.addFixing(floatSchedule[i], floatFix[i], true); //true=overwrite
}
CPICoupon zic = zisV.cpiLeg()[i] as CPICoupon;
if (zic != null)
{
if (zic.fixingDate() < (common.evaluationDate - new Period(1, TimeUnit.Months)))
{
fixedIndex.addFixing(zic.fixingDate(), cpiFix[i], true);
}
}
}
// simple structure so simple pricing engine - most work done by index
DiscountingSwapEngine dse = new DiscountingSwapEngine(common.nominalUK);
zisV.setPricingEngine(dse);
// get float+spread & fixed*inflation leg prices separately
double testInfLegNPV = 0.0;
double diff;
for (int i = 0; i < zisV.leg(0).Count; i++)
{
Date zicPayDate = (zisV.leg(0))[i].date();
if (zicPayDate > asofDate)
{
testInfLegNPV += (zisV.leg(0))[i].amount() * common.nominalUK.link.discount(zicPayDate);
}
CPICoupon zicV = zisV.cpiLeg()[i] as CPICoupon;
if (zicV != null)
{
diff = Math.Abs(zicV.rate() - (fixedRate * (zicV.indexFixing() / baseCPI)));
QAssert.IsTrue(diff < 1e-8, "failed " + i + "th coupon reconstruction as "
+ (fixedRate * (zicV.indexFixing() / baseCPI)) + " vs rate = "
+ zicV.rate() + ", with difference: " + diff);
}
}
double error = Math.Abs(testInfLegNPV - zisV.legNPV(0).Value);
QAssert.IsTrue(error < 1e-5, "failed manual inf leg NPV calc vs pricing engine: " + testInfLegNPV + " vs " +
zisV.legNPV(0));
diff = Math.Abs(1 - zisV.NPV() / 4191660.0);
#if QL_USE_INDEXED_COUPON
double max_diff = 1e-5;
#else
double max_diff = 3e-5;
#endif
QAssert.IsTrue(diff < max_diff, "failed stored consistency value test, ratio = " + diff);
// remove circular refernce
common.hcpi.linkTo(null);
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
/*********************
*** MARKET DATA ***
*********************/
Calendar calendar = new TARGET();
Date settlementDate = new Date(18, Month.September, 2008);
// must be a business day
settlementDate = calendar.adjust(settlementDate);
int fixingDays = 3;
int settlementDays = 3;
Date todaysDate = calendar.advance(settlementDate, -fixingDays, TimeUnit.Days);
// nothing to do with Date::todaysDate
Settings.setEvaluationDate(todaysDate);
Console.WriteLine("Today: {0}, {1}", todaysDate.DayOfWeek, todaysDate);
Console.WriteLine("Settlement date: {0}, {1}", settlementDate.DayOfWeek, settlementDate);
// Building of the bonds discounting yield curve
/*********************
*** RATE HELPERS ***
*********************/
// RateHelpers are built from the above quotes together with
// other instrument dependant infos. Quotes are passed in
// relinkable handles which could be relinked to some other
// data source later.
// Common data
// ZC rates for the short end
double zc3mQuote = 0.0096;
double zc6mQuote = 0.0145;
double zc1yQuote = 0.0194;
Quote zc3mRate = new SimpleQuote(zc3mQuote);
Quote zc6mRate = new SimpleQuote(zc6mQuote);
Quote zc1yRate = new SimpleQuote(zc1yQuote);
DayCounter zcBondsDayCounter = new Actual365Fixed();
RateHelper zc3m = new DepositRateHelper(new Handle <Quote>(zc3mRate),
new Period(3, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
RateHelper zc6m = new DepositRateHelper(new Handle <Quote>(zc6mRate),
new Period(6, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
RateHelper zc1y = new DepositRateHelper(new Handle <Quote>(zc1yRate),
new Period(1, TimeUnit.Years), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, zcBondsDayCounter);
// setup bonds
double redemption = 100.0;
const int numberOfBonds = 5;
Date[] issueDates =
{
new Date(15, Month.March, 2005),
new Date(15, Month.June, 2005),
new Date(30, Month.June, 2006),
new Date(15, Month.November, 2002),
new Date(15, Month.May, 1987)
};
Date[] maturities =
{
new Date(31, Month.August, 2010),
new Date(31, Month.August, 2011),
new Date(31, Month.August, 2013),
new Date(15, Month.August, 2018),
new Date(15, Month.May, 2038)
};
double[] couponRates =
{
0.02375,
0.04625,
0.03125,
0.04000,
0.04500
};
double[] marketQuotes =
{
100.390625,
106.21875,
100.59375,
101.6875,
102.140625
};
List <SimpleQuote> quote = new List <SimpleQuote>();
for (int i = 0; i < numberOfBonds; i++)
{
SimpleQuote cp = new SimpleQuote(marketQuotes[i]);
quote.Add(cp);
}
List <RelinkableHandle <Quote> > quoteHandle = new InitializedList <RelinkableHandle <Quote> >(numberOfBonds);
for (int i = 0; i < numberOfBonds; i++)
{
quoteHandle[i].linkTo(quote[i]);
}
// Definition of the rate helpers
List <FixedRateBondHelper> bondsHelpers = new List <FixedRateBondHelper>();
for (int i = 0; i < numberOfBonds; i++)
{
Schedule schedule = new Schedule(issueDates[i], maturities[i], new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted,
DateGeneration.Rule.Backward, false);
FixedRateBondHelper bondHelper = new FixedRateBondHelper(quoteHandle[i],
settlementDays,
100.0,
schedule,
new List <double>()
{
couponRates[i]
},
new ActualActual(ActualActual.Convention.Bond),
BusinessDayConvention.Unadjusted,
redemption,
issueDates[i]);
bondsHelpers.Add(bondHelper);
}
/*********************
** CURVE BUILDING **
*********************/
// Any DayCounter would be fine.
// ActualActual::ISDA ensures that 30 years is 30.0
DayCounter termStructureDayCounter = new ActualActual(ActualActual.Convention.ISDA);
double tolerance = 1.0e-15;
// A depo-bond curve
List <RateHelper> bondInstruments = new List <RateHelper>();
// Adding the ZC bonds to the curve for the short end
bondInstruments.Add(zc3m);
bondInstruments.Add(zc6m);
bondInstruments.Add(zc1y);
// Adding the Fixed rate bonds to the curve for the long end
for (int i = 0; i < numberOfBonds; i++)
{
bondInstruments.Add(bondsHelpers[i]);
}
YieldTermStructure bondDiscountingTermStructure = new PiecewiseYieldCurve <Discount, LogLinear>(
settlementDate, bondInstruments,
termStructureDayCounter,
new List <Handle <Quote> >(),
new List <Date>(),
tolerance);
// Building of the Libor forecasting curve
// deposits
double d1wQuote = 0.043375;
double d1mQuote = 0.031875;
double d3mQuote = 0.0320375;
double d6mQuote = 0.03385;
double d9mQuote = 0.0338125;
double d1yQuote = 0.0335125;
// swaps
double s2yQuote = 0.0295;
double s3yQuote = 0.0323;
double s5yQuote = 0.0359;
double s10yQuote = 0.0412;
double s15yQuote = 0.0433;
/********************
*** QUOTES ***
********************/
// SimpleQuote stores a value which can be manually changed;
// other Quote subclasses could read the value from a database
// or some kind of data feed.
// deposits
Quote d1wRate = new SimpleQuote(d1wQuote);
Quote d1mRate = new SimpleQuote(d1mQuote);
Quote d3mRate = new SimpleQuote(d3mQuote);
Quote d6mRate = new SimpleQuote(d6mQuote);
Quote d9mRate = new SimpleQuote(d9mQuote);
Quote d1yRate = new SimpleQuote(d1yQuote);
// swaps
Quote s2yRate = new SimpleQuote(s2yQuote);
Quote s3yRate = new SimpleQuote(s3yQuote);
Quote s5yRate = new SimpleQuote(s5yQuote);
Quote s10yRate = new SimpleQuote(s10yQuote);
Quote s15yRate = new SimpleQuote(s15yQuote);
/*********************
*** RATE HELPERS ***
*********************/
// RateHelpers are built from the above quotes together with
// other instrument dependant infos. Quotes are passed in
// relinkable handles which could be relinked to some other
// data source later.
// deposits
DayCounter depositDayCounter = new Actual360();
RateHelper d1w = new DepositRateHelper(
new Handle <Quote>(d1wRate),
new Period(1, TimeUnit.Weeks), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d1m = new DepositRateHelper(
new Handle <Quote>(d1mRate),
new Period(1, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d3m = new DepositRateHelper(
new Handle <Quote>(d3mRate),
new Period(3, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d6m = new DepositRateHelper(
new Handle <Quote>(d6mRate),
new Period(6, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d9m = new DepositRateHelper(
new Handle <Quote>(d9mRate),
new Period(9, TimeUnit.Months), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
RateHelper d1y = new DepositRateHelper(
new Handle <Quote>(d1yRate),
new Period(1, TimeUnit.Years), fixingDays,
calendar, BusinessDayConvention.ModifiedFollowing,
true, depositDayCounter);
// setup swaps
Frequency swFixedLegFrequency = Frequency.Annual;
BusinessDayConvention swFixedLegConvention = BusinessDayConvention.Unadjusted;
DayCounter swFixedLegDayCounter = new Thirty360(Thirty360.Thirty360Convention.European);
IborIndex swFloatingLegIndex = new Euribor6M();
Period forwardStart = new Period(1, TimeUnit.Days);
RateHelper s2y = new SwapRateHelper(
new Handle <Quote>(s2yRate), new Period(2, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
RateHelper s3y = new SwapRateHelper(
new Handle <Quote>(s3yRate), new Period(3, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
RateHelper s5y = new SwapRateHelper(
new Handle <Quote>(s5yRate), new Period(5, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
RateHelper s10y = new SwapRateHelper(
new Handle <Quote>(s10yRate), new Period(10, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
RateHelper s15y = new SwapRateHelper(
new Handle <Quote>(s15yRate), new Period(15, TimeUnit.Years),
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, new Handle <Quote>(), forwardStart);
/*********************
** CURVE BUILDING **
*********************/
// Any DayCounter would be fine.
// ActualActual::ISDA ensures that 30 years is 30.0
// A depo-swap curve
List <RateHelper> depoSwapInstruments = new List <RateHelper>();
depoSwapInstruments.Add(d1w);
depoSwapInstruments.Add(d1m);
depoSwapInstruments.Add(d3m);
depoSwapInstruments.Add(d6m);
depoSwapInstruments.Add(d9m);
depoSwapInstruments.Add(d1y);
depoSwapInstruments.Add(s2y);
depoSwapInstruments.Add(s3y);
depoSwapInstruments.Add(s5y);
depoSwapInstruments.Add(s10y);
depoSwapInstruments.Add(s15y);
YieldTermStructure depoSwapTermStructure = new PiecewiseYieldCurve <Discount, LogLinear>(
settlementDate, depoSwapInstruments,
termStructureDayCounter,
new List <Handle <Quote> >(),
new List <Date>(),
tolerance);
// Term structures that will be used for pricing:
// the one used for discounting cash flows
RelinkableHandle <YieldTermStructure> discountingTermStructure = new RelinkableHandle <YieldTermStructure>();
// the one used for forward rate forecasting
RelinkableHandle <YieldTermStructure> forecastingTermStructure = new RelinkableHandle <YieldTermStructure>();
/*********************
* BONDS TO BE PRICED *
**********************/
// Common data
double faceAmount = 100;
// Pricing engine
IPricingEngine bondEngine = new DiscountingBondEngine(discountingTermStructure);
// Zero coupon bond
ZeroCouponBond zeroCouponBond = new ZeroCouponBond(
settlementDays,
new UnitedStates(UnitedStates.Market.GovernmentBond),
faceAmount,
new Date(15, Month.August, 2013),
BusinessDayConvention.Following,
116.92,
new Date(15, Month.August, 2003));
zeroCouponBond.setPricingEngine(bondEngine);
// Fixed 4.5% US Treasury Note
Schedule fixedBondSchedule = new Schedule(new Date(15, Month.May, 2007),
new Date(15, Month.May, 2017), new Period(Frequency.Semiannual),
new UnitedStates(UnitedStates.Market.GovernmentBond),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, false);
FixedRateBond fixedRateBond = new FixedRateBond(
settlementDays,
faceAmount,
fixedBondSchedule,
new List <double>()
{
0.045
},
new ActualActual(ActualActual.Convention.Bond),
BusinessDayConvention.ModifiedFollowing,
100.0, new Date(15, Month.May, 2007));
fixedRateBond.setPricingEngine(bondEngine);
// Floating rate bond (3M USD Libor + 0.1%)
// Should and will be priced on another curve later...
RelinkableHandle <YieldTermStructure> liborTermStructure = new RelinkableHandle <YieldTermStructure>();
IborIndex libor3m = new USDLibor(new Period(3, TimeUnit.Months), liborTermStructure);
libor3m.addFixing(new Date(17, Month.July, 2008), 0.0278625);
Schedule floatingBondSchedule = new Schedule(new Date(21, Month.October, 2005),
new Date(21, Month.October, 2010), new Period(Frequency.Quarterly),
new UnitedStates(UnitedStates.Market.NYSE),
BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted, DateGeneration.Rule.Backward, true);
FloatingRateBond floatingRateBond = new FloatingRateBond(
settlementDays,
faceAmount,
floatingBondSchedule,
libor3m,
new Actual360(),
BusinessDayConvention.ModifiedFollowing,
2,
// Gearings
new List <double>()
{
1.0
},
// Spreads
new List <double>()
{
0.001
},
// Caps
new List <double>(),
// Floors
new List <double>(),
// Fixing in arrears
true,
100.0,
new Date(21, Month.October, 2005));
floatingRateBond.setPricingEngine(bondEngine);
// Coupon pricers
IborCouponPricer pricer = new BlackIborCouponPricer();
// optionLet volatilities
double volatility = 0.0;
Handle <OptionletVolatilityStructure> vol;
vol = new Handle <OptionletVolatilityStructure>(
new ConstantOptionletVolatility(
settlementDays,
calendar,
BusinessDayConvention.ModifiedFollowing,
volatility,
new Actual365Fixed()));
pricer.setCapletVolatility(vol);
Utils.setCouponPricer(floatingRateBond.cashflows(), pricer);
// Yield curve bootstrapping
forecastingTermStructure.linkTo(depoSwapTermStructure);
discountingTermStructure.linkTo(bondDiscountingTermStructure);
// We are using the depo & swap curve to estimate the future Libor rates
liborTermStructure.linkTo(depoSwapTermStructure);
/***************
* BOND PRICING *
****************/
// write column headings
int[] widths = { 18, 10, 10, 10 };
Console.WriteLine("{0,18}{1,10}{2,10}{3,10}", "", "ZC", "Fixed", "Floating");
string separator = " | ";
int width = widths[0]
+ widths[1]
+ widths[2]
+ widths[3];
string rule = "".PadLeft(width, '-'), dblrule = "".PadLeft(width, '=');
string tab = "".PadLeft(8, ' ');
Console.WriteLine(rule);
Console.WriteLine("Net present value".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.NPV(),
fixedRateBond.NPV(),
floatingRateBond.NPV());
Console.WriteLine("Clean price".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.cleanPrice(),
fixedRateBond.cleanPrice(),
floatingRateBond.cleanPrice());
Console.WriteLine("Dirty price".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.dirtyPrice(),
fixedRateBond.dirtyPrice(),
floatingRateBond.dirtyPrice());
Console.WriteLine("Accrued coupon".PadLeft(widths[0]) + "{0,10:n2}{1,10:n2}{2,10:n2}",
zeroCouponBond.accruedAmount(),
fixedRateBond.accruedAmount(),
floatingRateBond.accruedAmount());
Console.WriteLine("Previous coupon".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
"N/A",
fixedRateBond.previousCoupon(),
floatingRateBond.previousCoupon());
Console.WriteLine("Next coupon".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
"N/A",
fixedRateBond.nextCoupon(),
floatingRateBond.nextCoupon());
Console.WriteLine("Yield".PadLeft(widths[0]) + "{0,10:0.00%}{1,10:0.00%}{2,10:0.00%}",
zeroCouponBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
fixedRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
floatingRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual));
Console.WriteLine();
// Other computations
Console.WriteLine("Sample indirect computations (for the floating rate bond): ");
Console.WriteLine(rule);
Console.WriteLine("Yield to Clean Price: {0:n2}",
floatingRateBond.cleanPrice(floatingRateBond.yield(new Actual360(), Compounding.Compounded, Frequency.Annual),
new Actual360(), Compounding.Compounded, Frequency.Annual,
settlementDate));
Console.WriteLine("Clean Price to Yield: {0:0.00%}",
floatingRateBond.yield(floatingRateBond.cleanPrice(), new Actual360(), Compounding.Compounded, Frequency.Annual,
settlementDate));
/* "Yield to Price"
* "Price to Yield" */
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
//////////////// DATES //////////////////////////////////////////////
Calendar calendar = new TARGET();
Date todaysDate = new Date(15, Month.January, 2017);
Date settlementDate = new Date(todaysDate);
Settings.setEvaluationDate(todaysDate);
DayCounter dayCounter = new Actual365Fixed();
//////////////// MARKET //////////////////////////////////////////////
double underlying = 100.0;
double dividendYield = 0.035;
double riskFreeRate = 0.01;
double intensity = 0.02;
double volatility = 0.20;
Handle <YieldTermStructure> flatRfTermStructure = new Handle <YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
Handle <DefaultProbabilityTermStructure> flatHazardStructure = new Handle <DefaultProbabilityTermStructure>(new FlatHazardRate(settlementDate, intensity, dayCounter));
Period forwardStart = new Period(1, TimeUnit.Days);
DayCounter swFixedLegDayCounter = new Thirty360(Thirty360.Thirty360Convention.European);
IborIndex swFloatingLegIndex = new Euribor6M();
Handle <Quote> underlyingH = new Handle <Quote>(new SimpleQuote(underlying));
Handle <YieldTermStructure> flatDividendTS = new Handle <YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
Handle <BlackVolTermStructure> flatVolTS = new Handle <BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, volatility, dayCounter));
GeneralizedBlackScholesProcessTolerance bsmProcess = new GeneralizedBlackScholesProcessTolerance(underlyingH, flatDividendTS, flatRfTermStructure, flatVolTS);
Console.WriteLine("Underlying price = " + underlying);
Console.WriteLine("Risk-free interest rate = {0:0.00%}", riskFreeRate);
Console.WriteLine("Dividend yield = {0:0.00%}", dividendYield);
Console.WriteLine("Volatility = {0:0.00%}", volatility);
Console.Write("\n");
//////////////// SIMPLEX //////////////////////////////////////////////
/*
* CostFunction corstFunction = new CostFunction();
*
* List<double> X = new InitializedList<double>();
* X.Add(0.0);
* Vector vectX = new Vector (X);
*
* List<double> Dir = new InitializedList<double>();
* Dir.Add(1);
* Vector vectDir = new Vector (Dir);
*
* Constraint constraint = new PositiveConstraint();
* constraint
* Vector initValues = new Vector();
*
* Problem myProb = new Problem(corstFunction, constraint, initValues);
*/
//////////////// SURFACE //////////////////////////////////////////////
/*
* freeArbSVI testSurface = new freeArbSVI(strikesVol, timesVol, spotATP, flatTermStructure, flatDividendTS, blackVolMatrix,50);
*
* testSurface.matricesBuildingForwardMoneyness();
* testSurface.matricesBuildingTotalVariance();
* testSurface.matricesBuildingBSPrices();
* testSurface.splincalculation();
* testSurface.matricesBuildingA();
* testSurface.matricesBuildingB();
*/
//Console.WriteLine("value [0,0] = {0}", blackVolMatrix[1,1]);
// End test
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
public void calculate(GBMParaViewModel para)
{
// set up dates
Calendar calendar = new TARGET();
//Date todaysDate = new Date(DateTime.Now);
Date settlementDate = new Date(para.ReferenceDate_);
Settings.setEvaluationDate(settlementDate);
// our options
Option.Type type = this.callPutEnum_;
double underlying = para.CurrentPrice_;
double strike = this.strike_;
double dividendYield = para.Dividend_ / 100;
double riskFreeRate = para.Drift_ / 100;
double volatility = 0.0;
if (this.callPutEnum_ == Option.Type.Call)
{
try
{
volatility = para.Call_Interpolation_.value(this.strike_) / 100;
this.imVolCal_ = Math.Round(para.Call_Interpolation_.value(this.strike_), 1);
}
catch (Exception)
{
volatility = para.Call_Interpolation_.value(this.strike_, true) / 100;
this.imVolCal_ = Math.Round(para.Call_Interpolation_.value(this.strike_, true), 1);
}
}
else if (this.callPutEnum_ == Option.Type.Put)
{
try
{
volatility = para.Call_Interpolation_.value(this.strike_) / 100;
this.imVolCal_ = Math.Round(para.Put_Interpolation_.value(this.strike_), 1);
}
catch (Exception)
{
volatility = para.Call_Interpolation_.value(this.strike_, true) / 100;
this.imVolCal_ = Math.Round(para.Put_Interpolation_.value(this.strike_, true), 1);
}
}
Date maturity = new Date(this.maturiry_);
DayCounter dayCounter = new Actual365Fixed();
//// write column headings
//int[] widths = new int[] { 35, 14, 14, 14 };
//Console.Write("{0,-" + widths[0] + "}", "Method");
//Console.Write("{0,-" + widths[1] + "}", "European");
//Console.Write("{0,-" + widths[2] + "}", "Bermudan");
//Console.WriteLine("{0,-" + widths[3] + "}", "American");
//List<Date> exerciseDates = new List<Date>(); ;
//for (int i = 1; i <= 4; i++)
// exerciseDates.Add(settlementDate + new Period(3 * i, TimeUnit.Months));
Exercise europeanExercise = new EuropeanExercise(maturity);
//Exercise bermudanExercise = new BermudanExercise(exerciseDates);
//Exercise americanExercise = new AmericanExercise(settlementDate, maturity);
Handle <Quote> underlyingH = new Handle <Quote>(new SimpleQuote(underlying));
// bootstrap the yield/dividend/vol curves
var flatTermStructure = new Handle <YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
var flatDividendTS = new Handle <YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
var flatVolTS = new Handle <BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, volatility, dayCounter));
StrikedTypePayoff payoff = new PlainVanillaPayoff(type, strike);
var bsmProcess = new BlackScholesMertonProcess(underlyingH, flatDividendTS, flatTermStructure, flatVolTS);
// options
VanillaOption europeanOption = new VanillaOption(payoff, europeanExercise);
// Analytic formulas:
// Black-Scholes for European
europeanOption.setPricingEngine(new AnalyticEuropeanEngine(bsmProcess));
this.npv_ = Math.Round(europeanOption.NPV(), 6);
this.deltaCal_ = Math.Round(europeanOption.delta(), 6);
this.gammaCal_ = Math.Round(europeanOption.gamma(), 6);
this.vegaCal_ = Math.Round(europeanOption.vega() / 100, 6);
this.thetaCal_ = Math.Round(europeanOption.theta() / 365, 6);
this.rhoCal_ = Math.Round(europeanOption.rho() / 100, 6);
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
//////////////// DATES //////////////////////////////////////////////
Calendar calendar = new TARGET();
Date todaysDate = new Date(15, Month.January, 2017);
Date settlementDate = new Date(todaysDate);
Settings.setEvaluationDate(todaysDate);
DayCounter dayCounter = new Actual365Fixed();
//////////////// MARKET //////////////////////////////////////////////
// Spot
double underlying = 100;
Handle <Quote> underlyingH = new Handle <Quote>(new SimpleQuote(underlying));
// riskfree
double riskFreeRate = 0.01;
Handle <YieldTermStructure> flatTermStructure = new Handle <YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
// dividend
double dividendYield = 0.035;
double fixedDiv = 5.0;
Handle <YieldTermStructure> flatDividendTS = new Handle <YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
Handle <YieldTermStructure> FixedDivTermStructure = new Handle <YieldTermStructure>(new FixedForward(settlementDate, fixedDiv, underlying, dayCounter));
// flatvol
double volatility = 0.20;
Handle <BlackVolTermStructure> flatVolTS = new Handle <BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, volatility, dayCounter));
Console.WriteLine("Underlying price = " + underlying);
Console.WriteLine("Risk-free interest rate = {0:0.00%}", riskFreeRate);
Console.WriteLine("Dividend yield = {0:0.00%}", dividendYield);
Console.WriteLine("Flat Volatility = {0:0.00%}", volatility);
Console.Write("\n");
// volSurface
List <Date> datesVol = new InitializedList <Date>();
List <double> strikesVol = new InitializedList <double>();
double spotATP = 100;
Date StartDateVol = settlementDate + new Period(1, TimeUnit.Months);
Matrix blackVolMatrix = new Matrix(5, 5, 0.2);
List <double> timesVol = new InitializedList <double>();
for (int i = 0; i < blackVolMatrix.rows(); i++)
{
timesVol.Add(i + 1);
}
for (int j = 0; j < blackVolMatrix.columns(); j++)
{
datesVol.Add(StartDateVol + new Period(j, TimeUnit.Years));
for (int i = 0; i < blackVolMatrix.rows(); i++)
{
blackVolMatrix[i, j] = 0.2 + Math.Pow(2.5, (i)) / 100;
}
}
for (int j = 0; j < blackVolMatrix.columns(); j++)
{
strikesVol.Add(spotATP * (1 - (double)((int)(blackVolMatrix.rows() / 2)) / 10) + spotATP * 0.1 * j);
}
BlackVarianceSurface mySurface = new BlackVarianceSurface(settlementDate, calendar, datesVol,
strikesVol, blackVolMatrix, dayCounter);
Handle <BlackVolTermStructure> mySurfaceH = new Handle <BlackVolTermStructure>(mySurface);
// process
GeneralizedBlackScholesProcessTolerance bsmProcessVolSurface = new GeneralizedBlackScholesProcessTolerance(underlyingH, FixedDivTermStructure, flatTermStructure, mySurfaceH);
GeneralizedBlackScholesProcessTolerance bsmProcess = new GeneralizedBlackScholesProcessTolerance(underlyingH, flatDividendTS, flatTermStructure, flatVolTS);
//////////////// INSTRUMENT //////////////////////////////////////////////
double tolerance = 0.2;
List <Date> fixingdates = new InitializedList <Date>();
double coupon = 0.05;
double barrierlvl = 0.6;
for (int i = 1; i <= 4; i++)
{
fixingdates.Add(settlementDate + new Period(i, TimeUnit.Years));
}
GenericAutocall myGenericAutocall = new GenericAutocall(fixingdates, coupon, barrierlvl, underlying);
IPricingEngine mcengine = new MakeMGenericInstrument <PseudoRandom>(bsmProcessVolSurface)
.withAbsoluteTolerance(tolerance)
.withStepsPerYear(52)
.withSeed(50)
.value();
myGenericAutocall.setPricingEngine(mcengine);
//////////////// Printing Results //////////////////////////////////////////////
Console.WriteLine("NPV Generic Autocall = {0:0.0000}", myGenericAutocall.NPV());
Console.WriteLine("Err = {0:0.0000%}", myGenericAutocall.errorEstimate() / myGenericAutocall.NPV());
Console.WriteLine("Samples = {0}", myGenericAutocall.samples());
Console.Write("\n");
for (int i = 0; i < 4; i++)
{
Console.WriteLine("ProbaCall {1} = {0:0.0000%}", myGenericAutocall.inspout("ProbaCall " + i), i + 1);
}
Console.WriteLine("ProbaMid = {0:0.0000%}", myGenericAutocall.inspout("ProbaMid"));
Console.WriteLine("probaDown = {0:0.0000%}", myGenericAutocall.inspout("ProbaDown"));
Console.WriteLine("AvgDown/Proba = {0:0.0000%}", myGenericAutocall.inspout("AvgDown") / myGenericAutocall.inspout("ProbaDown"));
Console.Write("\n");
Console.WriteLine("Test - NoValue = {0:0.0000%}", myGenericAutocall.inspout("NoValue"));
// inspout() function
Console.Write("\n");
myGenericAutocall.inspout();
Console.Write("\n");
myGenericAutocall.inspout(2, true);
// End test
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
// set up dates
Calendar calendar = new TARGET();
Date todaysDate = new Date(15, Month.May, 1998);
Date settlementDate = new Date(17, Month.May, 1998);
Settings.setEvaluationDate(todaysDate);
// our options
Option.Type type = Option.Type.Put;
double underlying = 36;
double strike = 40;
double dividendYield = 0.00;
double riskFreeRate = 0.06;
double volatility = 0.20;
Date maturity = new Date(17, Month.May, 1999);
DayCounter dayCounter = new Actual365Fixed();
Console.WriteLine("Option type = " + type);
Console.WriteLine("Maturity = " + maturity);
Console.WriteLine("Underlying price = " + underlying);
Console.WriteLine("Strike = " + strike);
Console.WriteLine("Risk-free interest rate = {0:0.000000%}", riskFreeRate);
Console.WriteLine("Dividend yield = {0:0.000000%}", dividendYield);
Console.WriteLine("Volatility = {0:0.000000%}", volatility);
Console.Write("\n");
string method;
Console.Write("\n");
// write column headings
int[] widths = new int[]{ 35, 14, 14, 14 };
Console.Write("{0,-" + widths[0] + "}", "Method");
Console.Write("{0,-" + widths[1] + "}", "European");
Console.Write("{0,-" + widths[2] + "}", "Bermudan");
Console.WriteLine("{0,-" + widths[3] + "}", "American");
List<Date> exerciseDates = new List<Date>(); ;
for (int i = 1; i <= 4; i++)
exerciseDates.Add(settlementDate + new Period(3 * i, TimeUnit.Months));
Exercise europeanExercise = new EuropeanExercise(maturity);
Exercise bermudanExercise = new BermudanExercise(exerciseDates);
Exercise americanExercise = new AmericanExercise(settlementDate, maturity);
Handle<Quote> underlyingH = new Handle<Quote>(new SimpleQuote(underlying));
// bootstrap the yield/dividend/vol curves
var flatTermStructure = new Handle<YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
var flatDividendTS = new Handle<YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
var flatVolTS = new Handle<BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, volatility, dayCounter));
StrikedTypePayoff payoff = new PlainVanillaPayoff(type, strike);
var bsmProcess = new BlackScholesMertonProcess(underlyingH, flatDividendTS, flatTermStructure, flatVolTS);
// options
VanillaOption europeanOption = new VanillaOption(payoff, europeanExercise);
VanillaOption bermudanOption = new VanillaOption(payoff, bermudanExercise);
VanillaOption americanOption = new VanillaOption(payoff, americanExercise);
// Analytic formulas:
// Black-Scholes for European
method = "Black-Scholes";
europeanOption.setPricingEngine(new AnalyticEuropeanEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + "}", "N/A");
// Barone-Adesi and Whaley approximation for American
method = "Barone-Adesi/Whaley";
americanOption.setPricingEngine(new BaroneAdesiWhaleyApproximationEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + "}", "N/A");
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Bjerksund and Stensland approximation for American
method = "Bjerksund/Stensland";
americanOption.setPricingEngine(new BjerksundStenslandApproximationEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + "}", "N/A");
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Integral
method = "Integral";
europeanOption.setPricingEngine(new IntegralEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + "}", "N/A");
// Finite differences
int timeSteps = 801;
method = "Finite differences";
europeanOption.setPricingEngine(new FDEuropeanEngine(bsmProcess,timeSteps,timeSteps-1));
bermudanOption.setPricingEngine(new FDBermudanEngine(bsmProcess,timeSteps,timeSteps-1));
americanOption.setPricingEngine(new FDAmericanEngine(bsmProcess,timeSteps,timeSteps-1));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Jarrow-Rudd
method = "Binomial Jarrow-Rudd";
europeanOption.setPricingEngine(new BinomialVanillaEngine<JarrowRudd>(bsmProcess,timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<JarrowRudd>(bsmProcess,timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<JarrowRudd>(bsmProcess,timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
method = "Binomial Cox-Ross-Rubinstein";
europeanOption.setPricingEngine(new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Additive equiprobabilities
method = "Additive equiprobabilities";
europeanOption.setPricingEngine(new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Trigeorgis
method = "Binomial Trigeorgis";
europeanOption.setPricingEngine(new BinomialVanillaEngine<Trigeorgis>(bsmProcess,timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<Trigeorgis>(bsmProcess,timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<Trigeorgis>(bsmProcess,timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Tian
method = "Binomial Tian";
europeanOption.setPricingEngine(new BinomialVanillaEngine<Tian>(bsmProcess,timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<Tian>(bsmProcess,timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<Tian>(bsmProcess,timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Leisen-Reimer
method = "Binomial Leisen-Reimer";
europeanOption.setPricingEngine(new BinomialVanillaEngine<LeisenReimer>(bsmProcess,timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<LeisenReimer>(bsmProcess,timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<LeisenReimer>(bsmProcess,timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Joshi
method = "Binomial Joshi";
europeanOption.setPricingEngine(new BinomialVanillaEngine<Joshi4>(bsmProcess,timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<Joshi4>(bsmProcess,timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<Joshi4>(bsmProcess,timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Monte Carlo Method: MC (crude)
timeSteps = 1;
method = "MC (crude)";
ulong mcSeed = 42;
IPricingEngine mcengine1 = new MakeMCEuropeanEngine<PseudoRandom>(bsmProcess)
.withSteps(timeSteps)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed)
.value();
europeanOption.setPricingEngine(mcengine1);
// Real errorEstimate = europeanOption.errorEstimate();
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", "N/A");
// Monte Carlo Method: QMC (Sobol)
method = "QMC (Sobol)";
int nSamples = 32768; // 2^15
IPricingEngine mcengine2 = new MakeMCEuropeanEngine<LowDiscrepancy>(bsmProcess)
.withSteps(timeSteps)
.withSamples(nSamples)
.value();
europeanOption.setPricingEngine(mcengine2);
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", "N/A");
// Monte Carlo Method: MC (Longstaff Schwartz)
method = "MC (Longstaff Schwartz)";
IPricingEngine mcengine3 = new MakeMCAmericanEngine<PseudoRandom>(bsmProcess)
.withSteps(100)
.withAntitheticVariate()
.withCalibrationSamples(4096)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed)
.value();
americanOption.setPricingEngine(mcengine3);
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", "N/A");
Console.Write("{0,-" + widths[2] + ":0.000000}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// End test
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
/// <summary>
/// Evaluates the specified option contract to compute a theoretical price, IV and greeks
/// </summary>
/// <param name="security">The option security object</param>
/// <param name="slice">The current data slice. This can be used to access other information
/// available to the algorithm</param>
/// <param name="contract">The option contract to evaluate</param>
/// <returns>An instance of <see cref="OptionPriceModelResult"/> containing the theoretical
/// price of the specified option contract</returns>
public OptionPriceModelResult Evaluate(Security security, Slice slice, OptionContract contract)
{
try
{
// setting up option pricing parameters
var calendar = new UnitedStates();
var dayCounter = new Actual365Fixed();
var optionSecurity = (Option)security;
var settlementDate = contract.Time.Date.AddDays(Option.DefaultSettlementDays);
var maturityDate = contract.Expiry.Date.AddDays(Option.DefaultSettlementDays);
var underlyingQuoteValue = new SimpleQuote((double)optionSecurity.Underlying.Price);
var dividendYieldValue = new SimpleQuote(_dividendYieldEstimator.Estimate(security, slice, contract));
var dividendYield = new Handle <YieldTermStructure>(new FlatForward(0, calendar, dividendYieldValue, dayCounter));
var riskFreeRateValue = new SimpleQuote(_riskFreeRateEstimator.Estimate(security, slice, contract));
var riskFreeRate = new Handle <YieldTermStructure>(new FlatForward(0, calendar, riskFreeRateValue, dayCounter));
var underlyingVolValue = new SimpleQuote(_underlyingVolEstimator.Estimate(security, slice, contract));
var underlyingVol = new Handle <BlackVolTermStructure>(new BlackConstantVol(0, calendar, new Handle <Quote>(underlyingVolValue), dayCounter));
// preparing stochastic process and payoff functions
var stochasticProcess = new BlackScholesMertonProcess(new Handle <Quote>(underlyingQuoteValue), dividendYield, riskFreeRate, underlyingVol);
var payoff = new PlainVanillaPayoff(contract.Right == OptionRight.Call ? QLNet.Option.Type.Call : QLNet.Option.Type.Put, (double)contract.Strike);
// creating option QL object
var option = contract.Symbol.ID.OptionStyle == OptionStyle.American ?
new VanillaOption(payoff, new AmericanExercise(settlementDate, maturityDate)) :
new VanillaOption(payoff, new EuropeanExercise(maturityDate));
Settings.setEvaluationDate(settlementDate);
// preparing pricing engine QL object
option.setPricingEngine(_pricingEngineFunc(contract.Symbol, stochasticProcess));
// running calculations
var npv = EvaluateOption(option);
// function extracts QL greeks catching exception if greek is not generated by the pricing engine and reevaluates option to get numerical estimate of the seisitivity
Func <Func <double>, Func <double>, decimal> tryGetGreekOrReevaluate = (greek, reevalFunc) =>
{
try
{
return((decimal)greek());
}
catch (Exception)
{
return(optionSecurity.EnableGreekApproximation ? (decimal)reevalFunc() : 0.0m);
}
};
// function extracts QL greeks catching exception if greek is not generated by the pricing engine
Func <Func <double>, decimal> tryGetGreek = greek => tryGetGreekOrReevaluate(greek, () => 0.0);
// function extracts QL IV catching exception if IV is not generated by the pricing engine
Func <decimal> tryGetImpliedVol = () =>
{
try
{
return((decimal)option.impliedVolatility((double)optionSecurity.Price, stochasticProcess));
}
catch (Exception err)
{
Log.Debug("tryGetImpliedVol() error: " + err.Message);
return(0m);
}
};
Func <Tuple <decimal, decimal> > evalDeltaGamma = () =>
{
try
{
return(Tuple.Create((decimal)option.delta(), (decimal)option.gamma()));
}
catch (Exception)
{
if (optionSecurity.EnableGreekApproximation)
{
var step = 0.01;
var initial = underlyingQuoteValue.value();
underlyingQuoteValue.setValue(initial - step);
var npvMinus = EvaluateOption(option);
underlyingQuoteValue.setValue(initial + step);
var npvPlus = EvaluateOption(option);
underlyingQuoteValue.setValue(initial);
return(Tuple.Create((decimal)((npvPlus - npvMinus) / (2 * step)),
(decimal)((npvPlus - 2 * npv + npvMinus) / (step * step))));
}
else
{
return(Tuple.Create(0.0m, 0.0m));
}
}
};
Func <double> reevalVega = () =>
{
var step = 0.001;
var initial = underlyingVolValue.value();
underlyingVolValue.setValue(initial + step);
var npvPlus = EvaluateOption(option);
underlyingVolValue.setValue(initial);
return((npvPlus - npv) / step);
};
Func <double> reevalTheta = () =>
{
var step = 1.0 / 365.0;
Settings.setEvaluationDate(settlementDate.AddDays(-1));
var npvMinus = EvaluateOption(option);
Settings.setEvaluationDate(settlementDate);
return((npv - npvMinus) / step);
};
Func <double> reevalRho = () =>
{
var step = 0.001;
var initial = riskFreeRateValue.value();
riskFreeRateValue.setValue(initial + step);
var npvPlus = EvaluateOption(option);
riskFreeRateValue.setValue(initial);
return((npvPlus - npv) / step);
};
// producing output with lazy calculations of IV and greeks
return(new OptionPriceModelResult((decimal)npv,
tryGetImpliedVol,
() => new Greeks(evalDeltaGamma,
() => tryGetGreekOrReevaluate(() => option.vega(), reevalVega),
() => tryGetGreekOrReevaluate(() => option.theta(), reevalTheta),
() => tryGetGreekOrReevaluate(() => option.rho(), reevalRho),
() => tryGetGreek(() => option.elasticity()))));
}
catch (Exception err)
{
Log.Debug("QLOptionPriceModel.Evaluate() error: " + err.Message);
return(new OptionPriceModelResult(0m, new Greeks()));
}
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
// set up dates
Calendar calendar = new TARGET();
Date todaysDate = new Date(15, Month.May, 1998);
Date settlementDate = new Date(17, Month.May, 1998);
Settings.setEvaluationDate(todaysDate);
// our options
Option.Type type = Option.Type.Put;
double underlying = 36;
double strike = 40;
double dividendYield = 0.00;
double riskFreeRate = 0.06;
double volatility = 0.20;
Date maturity = new Date(17, Month.May, 1999);
DayCounter dayCounter = new Actual365Fixed();
Console.WriteLine("Option type = " + type);
Console.WriteLine("Maturity = " + maturity);
Console.WriteLine("Underlying price = " + underlying);
Console.WriteLine("Strike = " + strike);
Console.WriteLine("Risk-free interest rate = {0:0.000000%}", riskFreeRate);
Console.WriteLine("Dividend yield = {0:0.000000%}", dividendYield);
Console.WriteLine("Volatility = {0:0.000000%}", volatility);
Console.Write("\n");
string method;
Console.Write("\n");
// write column headings
int[] widths = new int[] { 35, 14, 14, 14 };
Console.Write("{0,-" + widths[0] + "}", "Method");
Console.Write("{0,-" + widths[1] + "}", "European");
Console.Write("{0,-" + widths[2] + "}", "Bermudan");
Console.WriteLine("{0,-" + widths[3] + "}", "American");
List <Date> exerciseDates = new List <Date>();;
for (int i = 1; i <= 4; i++)
{
exerciseDates.Add(settlementDate + new Period(3 * i, TimeUnit.Months));
}
Exercise europeanExercise = new EuropeanExercise(maturity);
Exercise bermudanExercise = new BermudanExercise(exerciseDates);
Exercise americanExercise = new AmericanExercise(settlementDate, maturity);
Handle <Quote> underlyingH = new Handle <Quote>(new SimpleQuote(underlying));
// bootstrap the yield/dividend/vol curves
var flatTermStructure = new Handle <YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
var flatDividendTS = new Handle <YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
var flatVolTS = new Handle <BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, volatility, dayCounter));
StrikedTypePayoff payoff = new PlainVanillaPayoff(type, strike);
var bsmProcess = new BlackScholesMertonProcess(underlyingH, flatDividendTS, flatTermStructure, flatVolTS);
// options
VanillaOption europeanOption = new VanillaOption(payoff, europeanExercise);
VanillaOption bermudanOption = new VanillaOption(payoff, bermudanExercise);
VanillaOption americanOption = new VanillaOption(payoff, americanExercise);
// Analytic formulas:
// Black-Scholes for European
method = "Black-Scholes";
europeanOption.setPricingEngine(new AnalyticEuropeanEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + "}", "N/A");
// Barone-Adesi and Whaley approximation for American
method = "Barone-Adesi/Whaley";
americanOption.setPricingEngine(new BaroneAdesiWhaleyApproximationEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + "}", "N/A");
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Bjerksund and Stensland approximation for American
method = "Bjerksund/Stensland";
americanOption.setPricingEngine(new BjerksundStenslandApproximationEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + "}", "N/A");
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Integral
method = "Integral";
europeanOption.setPricingEngine(new IntegralEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + "}", "N/A");
// Finite differences
int timeSteps = 801;
method = "Finite differences";
europeanOption.setPricingEngine(new FDEuropeanEngine(bsmProcess, timeSteps, timeSteps - 1));
bermudanOption.setPricingEngine(new FDBermudanEngine(bsmProcess, timeSteps, timeSteps - 1));
americanOption.setPricingEngine(new FDAmericanEngine(bsmProcess, timeSteps, timeSteps - 1));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Jarrow-Rudd
method = "Binomial Jarrow-Rudd";
europeanOption.setPricingEngine(new BinomialVanillaEngine <JarrowRudd>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine <JarrowRudd>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine <JarrowRudd>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
method = "Binomial Cox-Ross-Rubinstein";
europeanOption.setPricingEngine(new BinomialVanillaEngine <CoxRossRubinstein>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine <CoxRossRubinstein>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine <CoxRossRubinstein>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Additive equiprobabilities
method = "Additive equiprobabilities";
europeanOption.setPricingEngine(new BinomialVanillaEngine <AdditiveEQPBinomialTree>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine <AdditiveEQPBinomialTree>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine <AdditiveEQPBinomialTree>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Trigeorgis
method = "Binomial Trigeorgis";
europeanOption.setPricingEngine(new BinomialVanillaEngine <Trigeorgis>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine <Trigeorgis>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine <Trigeorgis>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Tian
method = "Binomial Tian";
europeanOption.setPricingEngine(new BinomialVanillaEngine <Tian>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine <Tian>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine <Tian>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Leisen-Reimer
method = "Binomial Leisen-Reimer";
europeanOption.setPricingEngine(new BinomialVanillaEngine <LeisenReimer>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine <LeisenReimer>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine <LeisenReimer>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Joshi
method = "Binomial Joshi";
europeanOption.setPricingEngine(new BinomialVanillaEngine <Joshi4>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine <Joshi4>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine <Joshi4>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Monte Carlo Method: MC (crude)
timeSteps = 1;
method = "MC (crude)";
ulong mcSeed = 42;
IPricingEngine mcengine1 = new MakeMCEuropeanEngine <PseudoRandom>(bsmProcess)
.withSteps(timeSteps)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed)
.value();
europeanOption.setPricingEngine(mcengine1);
// Real errorEstimate = europeanOption.errorEstimate();
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", "N/A");
// Monte Carlo Method: QMC (Sobol)
method = "QMC (Sobol)";
int nSamples = 32768; // 2^15
IPricingEngine mcengine2 = new MakeMCEuropeanEngine <LowDiscrepancy>(bsmProcess)
.withSteps(timeSteps)
.withSamples(nSamples)
.value();
europeanOption.setPricingEngine(mcengine2);
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", "N/A");
// Monte Carlo Method: MC (Longstaff Schwartz)
method = "MC (Longstaff Schwartz)";
IPricingEngine mcengine3 = new MakeMCAmericanEngine <PseudoRandom>(bsmProcess)
.withSteps(100)
.withAntitheticVariate()
.withCalibrationSamples(4096)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed)
.value();
americanOption.setPricingEngine(mcengine3);
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", "N/A");
Console.Write("{0,-" + widths[2] + ":0.000000}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// End test
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
public void testImpliedHazardRate()
{
// Testing implied hazard-rate for credit-default swaps...
using (SavedSettings backup = new SavedSettings())
{
// Initialize curves
Calendar calendar = new TARGET();
Date today = calendar.adjust(Date.Today);
Settings.setEvaluationDate(today);
double h1 = 0.30, h2 = 0.40;
DayCounter dayCounter = new Actual365Fixed();
List <Date> dates = new List <Date>(3);
List <double> hazardRates = new List <double>(3);
dates.Add(today);
hazardRates.Add(h1);
dates.Add(today + new Period(5, TimeUnit.Years));
hazardRates.Add(h1);
dates.Add(today + new Period(10, TimeUnit.Years));
hazardRates.Add(h2);
RelinkableHandle <DefaultProbabilityTermStructure> probabilityCurve =
new RelinkableHandle <DefaultProbabilityTermStructure>();
probabilityCurve.linkTo(new InterpolatedHazardRateCurve <BackwardFlat>(dates,
hazardRates,
dayCounter));
RelinkableHandle <YieldTermStructure> discountCurve = new RelinkableHandle <YieldTermStructure>();
discountCurve.linkTo(new FlatForward(today, 0.03, new Actual360()));
Frequency frequency = Frequency.Semiannual;
BusinessDayConvention convention = BusinessDayConvention.ModifiedFollowing;
Date issueDate = calendar.advance(today, -6, TimeUnit.Months);
double fixedRate = 0.0120;
DayCounter cdsDayCount = new Actual360();
double notional = 10000.0;
double recoveryRate = 0.4;
double?latestRate = null;
for (int n = 6; n <= 10; ++n)
{
Date maturity = calendar.advance(issueDate, n, TimeUnit.Years);
Schedule schedule = new Schedule(issueDate, maturity, new Period(frequency), calendar,
convention, convention,
DateGeneration.Rule.Forward, false);
CreditDefaultSwap cds = new CreditDefaultSwap(Protection.Side.Seller, notional, fixedRate,
schedule, convention, cdsDayCount, true, true);
cds.setPricingEngine(new MidPointCdsEngine(probabilityCurve, recoveryRate, discountCurve));
double NPV = cds.NPV();
double flatRate = cds.impliedHazardRate(NPV, discountCurve,
dayCounter,
recoveryRate);
if (flatRate < h1 || flatRate > h2)
{
QAssert.Fail("implied hazard rate outside expected range\n"
+ " maturity: " + n + " years\n"
+ " expected minimum: " + h1 + "\n"
+ " expected maximum: " + h2 + "\n"
+ " implied rate: " + flatRate);
}
if (n > 6 && flatRate < latestRate)
{
QAssert.Fail("implied hazard rate decreasing with swap maturity\n"
+ " maturity: " + n + " years\n"
+ " previous rate: " + latestRate + "\n"
+ " implied rate: " + flatRate);
}
latestRate = flatRate;
RelinkableHandle <DefaultProbabilityTermStructure> probability = new RelinkableHandle <DefaultProbabilityTermStructure>();
probability.linkTo(new FlatHazardRate(today, new Handle <Quote>(new SimpleQuote(flatRate)), dayCounter));
CreditDefaultSwap cds2 = new CreditDefaultSwap(Protection.Side.Seller, notional, fixedRate,
schedule, convention, cdsDayCount, true, true);
cds2.setPricingEngine(new MidPointCdsEngine(probability, recoveryRate, discountCurve));
double NPV2 = cds2.NPV();
double tolerance = 1.0;
if (Math.Abs(NPV - NPV2) > tolerance)
{
QAssert.Fail("failed to reproduce NPV with implied rate\n"
+ " expected: " + NPV + "\n"
+ " calculated: " + NPV2);
}
}
}
}
public void testFdmHestonVarianceMesher()
{
//Testing FDM Heston variance mesher...
using (SavedSettings backup = new SavedSettings())
{
Date today = new Date(22, 2, 2018);
DayCounter dc = new Actual365Fixed();
Settings.Instance.setEvaluationDate(today);
HestonProcess process = new HestonProcess(new Handle <YieldTermStructure>(Utilities.flatRate(0.02, dc)),
new Handle <YieldTermStructure>(Utilities.flatRate(0.02, dc)),
new Handle <Quote>(new SimpleQuote(100.0)),
0.09, 1.0, 0.09, 0.2, -0.5);
FdmHestonVarianceMesher mesher = new FdmHestonVarianceMesher(5, process, 1.0);
List <double> locations = mesher.locations();
double[] expected = new double[] { 0.0, 6.652314e-02, 9.000000e-02, 1.095781e-01, 2.563610e-01 };
double tol = 1e-6;
double diff;
for (int i = 0; i < locations.Count; ++i)
{
diff = Math.Abs(expected[i] - locations[i]);
if (diff > tol)
{
QAssert.Fail("Failed to reproduce Heston variance mesh"
+ "\n calculated: " + locations[i]
+ "\n expected: " + expected[i]
+ "\n difference " + diff
+ "\n tolerance: " + tol);
}
}
LocalVolTermStructure lVol = new LocalConstantVol(today, 2.5, dc);
FdmHestonLocalVolatilityVarianceMesher constSlvMesher = new FdmHestonLocalVolatilityVarianceMesher(5, process, lVol, 1.0);
double expectedVol = 2.5 * mesher.volaEstimate();
double calculatedVol = constSlvMesher.volaEstimate();
diff = Math.Abs(calculatedVol - expectedVol);
if (diff > tol)
{
QAssert.Fail("Failed to reproduce Heston local volatility variance estimate"
+ "\n calculated: " + calculatedVol
+ "\n expected: " + expectedVol
+ "\n difference " + diff
+ "\n tolerance: " + tol);
}
double alpha = 0.01;
LocalVolTermStructure leverageFct = new ParableLocalVolatility(today, 100.0, alpha, dc);
FdmHestonLocalVolatilityVarianceMesher slvMesher
= new FdmHestonLocalVolatilityVarianceMesher(5, process, leverageFct, 0.5, 1, 0.01);
double initialVolEstimate = new FdmHestonVarianceMesher(5, process, 0.5, 1, 0.01).volaEstimate();
// double vEst = leverageFct.currentLink().localVol(0, 100) * initialVolEstimate;
// Mathematica solution
// N[Integrate[
// alpha*((100*Exp[vEst*x*Sqrt[0.5]] - 100)^2 + 25)*
// PDF[NormalDistribution[0, 1], x], {x ,
// InverseCDF[NormalDistribution[0, 1], 0.01],
// InverseCDF[NormalDistribution[0, 1], 0.99]}]]
double leverageAvg = 0.455881 / (1 - 0.02);
double volaEstExpected =
0.5 * (leverageAvg + leverageFct.localVol(0, 100)) * initialVolEstimate;
double volaEstCalculated = slvMesher.volaEstimate();
if (Math.Abs(volaEstExpected - volaEstCalculated) > 0.001)
{
QAssert.Fail("Failed to reproduce Heston local volatility variance estimate"
+ "\n calculated: " + calculatedVol
+ "\n expected: " + expectedVol
+ "\n difference " + Math.Abs(volaEstExpected - volaEstCalculated)
+ "\n tolerance: " + tol);
}
}
}
public void cpibondconsistency()
{
CommonVars common = new CommonVars();
// ZeroInflationSwap aka CPISwap
CPISwap.Type type = CPISwap.Type.Payer;
double nominal = 1000000.0;
bool subtractInflationNominal = true;
// float+spread leg
double spread = 0.0;
DayCounter floatDayCount = new Actual365Fixed();
BusinessDayConvention floatPaymentConvention = BusinessDayConvention.ModifiedFollowing;
int fixingDays = 0;
IborIndex floatIndex = new GBPLibor(new Period(6, TimeUnit.Months), common.nominalUK);
// fixed x inflation leg
double fixedRate = 0.1; //1% would be 0.01
double baseCPI = 206.1; // would be 206.13871 if we were interpolating
DayCounter fixedDayCount = new Actual365Fixed();
BusinessDayConvention fixedPaymentConvention = BusinessDayConvention.ModifiedFollowing;
Calendar fixedPaymentCalendar = new UnitedKingdom();
ZeroInflationIndex fixedIndex = common.ii;
Period contractObservationLag = common.contractObservationLag;
InterpolationType observationInterpolation = common.contractObservationInterpolation;
// set the schedules
Date startDate = new Date(2, Month.October, 2007);
Date endDate = new Date(2, Month.October, 2052);
Schedule floatSchedule = new MakeSchedule().from(startDate).to(endDate)
.withTenor(new Period(6, TimeUnit.Months))
.withCalendar(new UnitedKingdom())
.withConvention(floatPaymentConvention)
.backwards().value();
Schedule fixedSchedule = new MakeSchedule().from(startDate).to(endDate)
.withTenor(new Period(6, TimeUnit.Months))
.withCalendar(new UnitedKingdom())
.withConvention(BusinessDayConvention.Unadjusted)
.backwards().value();
CPISwap zisV = new CPISwap(type, nominal, subtractInflationNominal,
spread, floatDayCount, floatSchedule,
floatPaymentConvention, fixingDays, floatIndex,
fixedRate, baseCPI, fixedDayCount, fixedSchedule,
fixedPaymentConvention, contractObservationLag,
fixedIndex, observationInterpolation);
double[] floatFix = { 0.06255, 0.05975, 0.0637, 0.018425, 0.0073438, -1, -1 };
double[] cpiFix = { 211.4, 217.2, 211.4, 213.4, -2, -2 };
for (int i = 0; i < floatSchedule.Count; i++)
{
if (floatSchedule[i] < common.evaluationDate)
{
floatIndex.addFixing(floatSchedule[i], floatFix[i], true); //true=overwrite
}
CPICoupon zic = zisV.cpiLeg()[i] as CPICoupon;
if (zic != null)
{
if (zic.fixingDate() < (common.evaluationDate - new Period(1, TimeUnit.Months)))
{
fixedIndex.addFixing(zic.fixingDate(), cpiFix[i], true);
}
}
}
// simple structure so simple pricing engine - most work done by index
DiscountingSwapEngine dse = new DiscountingSwapEngine(common.nominalUK);
zisV.setPricingEngine(dse);
// now do the bond equivalent
List <double> fixedRates = new InitializedList <double>(1, fixedRate);
int settlementDays = 1;// cannot be zero!
bool growthOnly = true;
CPIBond cpiB = new CPIBond(settlementDays, nominal, growthOnly,
baseCPI, contractObservationLag, fixedIndex,
observationInterpolation, fixedSchedule,
fixedRates, fixedDayCount, fixedPaymentConvention);
DiscountingBondEngine dbe = new DiscountingBondEngine(common.nominalUK);
cpiB.setPricingEngine(dbe);
QAssert.IsTrue(Math.Abs(cpiB.NPV() - zisV.legNPV(0).GetValueOrDefault()) < 1e-5,
"cpi bond does not equal equivalent cpi swap leg");
// remove circular refernce
common.hcpi.linkTo(null);
}
public void testFdmHestonBarrierVsBlackScholes()
{
//Testing FDM with barrier option in Heston model...
using (SavedSettings backup = new SavedSettings())
{
NewBarrierOptionData[] values = new NewBarrierOptionData[] {
/* The data below are from
* "Option pricing formulas", E.G. Haug, McGraw-Hill 1998 pag. 72
*/
// barrierType, barrier, rebate, type, strike, s, q, r, t, v
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Call, 100, 100.0, 0.00, 0.08, 1.00, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Call, 90, 100.0, 0.00, 0.08, 0.25, 0.25),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Call, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Call, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Call, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Call, 90, 100.0, 0.00, 0.08, 0.25, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Call, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Call, 100, 100.0, 0.00, 0.08, 0.40, 0.25),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.15),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Call, 100, 100.0, 0.00, 0.08, 0.40, 0.35),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.15),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Call, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Call, 110, 100.0, 0.00, 0.00, 1.00, 0.20),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Call, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Call, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Call, 110, 100.0, 0.00, 0.08, 1.00, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Call, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Call, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Call, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Call, 110, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.25),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Put, 110, 100.0, 0.00, 0.04, 1.00, 0.15),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 95.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownOut, 100.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpOut, 105.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 95.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.DownIn, 100.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 1.00, 0.15),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Put, 90, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Put, 100, 100.0, 0.04, 0.08, 0.50, 0.30),
new NewBarrierOptionData(Barrier.Type.UpIn, 105.0, 3.0, Option.Type.Put, 110, 100.0, 0.04, 0.08, 0.50, 0.30)
};
DayCounter dc = new Actual365Fixed();
Date todaysDate = new Date(28, 3, 2004);
Date exerciseDate = new Date(28, 3, 2005);
Settings.Instance.setEvaluationDate(todaysDate);
Handle <Quote> spot = new Handle <Quote>(new SimpleQuote(0.0));
SimpleQuote qRate = new SimpleQuote(0.0);
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(qRate, dc));
SimpleQuote rRate = new SimpleQuote(0.0);
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(rRate, dc));
SimpleQuote vol = new SimpleQuote(0.0);
Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(vol, dc));
BlackScholesMertonProcess bsProcess = new BlackScholesMertonProcess(spot, qTS, rTS, volTS);
IPricingEngine analyticEngine = new AnalyticBarrierEngine(bsProcess);
for (int i = 0; i < values.Length; i++)
{
Date exDate = todaysDate + Convert.ToInt32(values[i].t * 365 + 0.5);
Exercise exercise = new EuropeanExercise(exDate);
(spot.currentLink() as SimpleQuote).setValue(values[i].s);
qRate.setValue(values[i].q);
rRate.setValue(values[i].r);
vol.setValue(values[i].v);
StrikedTypePayoff payoff = new PlainVanillaPayoff(values[i].type, values[i].strike);
BarrierOption barrierOption = new BarrierOption(values[i].barrierType, values[i].barrier,
values[i].rebate, payoff, exercise);
double v0 = vol.value() * vol.value();
HestonProcess hestonProcess =
new HestonProcess(rTS, qTS, spot, v0, 1.0, v0, 0.005, 0.0);
barrierOption.setPricingEngine(new FdHestonBarrierEngine(new HestonModel(hestonProcess), 200, 101, 3));
double calculatedHE = barrierOption.NPV();
barrierOption.setPricingEngine(analyticEngine);
double expected = barrierOption.NPV();
double tol = 0.0025;
if (Math.Abs(calculatedHE - expected) / expected > tol)
{
QAssert.Fail("Failed to reproduce expected Heston npv"
+ "\n calculated: " + calculatedHE
+ "\n expected: " + expected
+ "\n tolerance: " + tol);
}
}
}
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(Actual365Fixed obj) {
return (obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr;
}
static void Main(string[] args)
{
try
{
DateTime timer = DateTime.Now;
Option.Type type = Option.Type.Put;
double underlying = 36.0;
double spreadRate = 0.005;
double dividendYield = 0.02;
double riskFreeRate = 0.06;
double volatility = 0.2;
int settlementDays = 3;
int length = 5;
double redemption = 100.0;
double conversionRatio = redemption / underlying; // at the money
// set up dates/schedules
Calendar calendar = new TARGET();
Date today = calendar.adjust(Date.Today);
Settings.setEvaluationDate(today);
Date settlementDate = calendar.advance(today, settlementDays, TimeUnit.Days);
Date exerciseDate = calendar.advance(settlementDate, length, TimeUnit.Years);
Date issueDate = calendar.advance(exerciseDate, -length, TimeUnit.Years);
BusinessDayConvention convention = BusinessDayConvention.ModifiedFollowing;
Frequency frequency = Frequency.Annual;
Schedule schedule = new Schedule(issueDate, exerciseDate,
new Period(frequency), calendar, convention, convention,
DateGeneration.Rule.Backward, false);
DividendSchedule dividends = new DividendSchedule();
CallabilitySchedule callability = new CallabilitySchedule();
List <double> coupons = new InitializedList <double>(1, 0.05);
DayCounter bondDayCount = new Thirty360();
int[] callLength = { 2, 4 }; // Call dates, years 2,4.
int[] putLength = { 3 }; // Put dates year 3.
double[] callPrices = { 101.5, 100.85 };
double[] putPrices = { 105.0 };
// Load call schedules
for (int i = 0; i < callLength.Length; i++)
{
SoftCallability s = new SoftCallability(
new Callability.Price(callPrices[i], Callability.Price.Type.Clean), schedule.date(callLength[i]),
1.20);
callability.Add(s);
}
for (int j = 0; j < putLength.Length; j++)
{
Callability s = new Callability(new Callability.Price(putPrices[j], Callability.Price.Type.Clean),
Callability.Type.Put, schedule.date(putLength[j]));
callability.Add(s);
}
// Assume dividends are paid every 6 months .
for (Date d = today + new Period(6, TimeUnit.Months); d < exerciseDate; d += new Period(6, TimeUnit.Months))
{
Dividend div = new FixedDividend(1.0, d);
dividends.Add(div);
}
DayCounter dayCounter = new Actual365Fixed();
double maturity = dayCounter.yearFraction(settlementDate, exerciseDate);
Console.WriteLine("option type = " + type);
Console.WriteLine("Time to maturity = " + maturity);
Console.WriteLine("Underlying price = " + underlying);
Console.WriteLine("Risk-free interest rate = {0:0.0%}", riskFreeRate);
Console.WriteLine("Dividend yield = {0:0.0%}%", dividendYield);
Console.WriteLine("Volatility = {0:0.0%}%", volatility);
Console.WriteLine("");
// write column headings
int[] widths = { 35, 14, 14 };
int totalWidth = widths[0] + widths[1] + widths[2];
string rule = new string('-', totalWidth);
string dblrule = new string('=', totalWidth);
Console.WriteLine(dblrule);
Console.WriteLine("Tsiveriotis-Fernandes method");
Console.WriteLine(dblrule);
Console.WriteLine("Tree Type European American ");
Console.WriteLine(rule);
Exercise exercise = new EuropeanExercise(exerciseDate);
Exercise amexercise = new AmericanExercise(settlementDate, exerciseDate);
Handle <Quote> underlyingH = new Handle <Quote>(new SimpleQuote(underlying));
Handle <YieldTermStructure> flatTermStructure =
new Handle <YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
Handle <YieldTermStructure> flatDividendTS =
new Handle <YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
Handle <BlackVolTermStructure> flatVolTS =
new Handle <BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, volatility,
dayCounter));
BlackScholesMertonProcess stochasticProcess =
new BlackScholesMertonProcess(underlyingH, flatDividendTS, flatTermStructure, flatVolTS);
int timeSteps = 801;
Handle <Quote> creditSpread = new Handle <Quote>(new SimpleQuote(spreadRate));
Quote rate = new SimpleQuote(riskFreeRate);
Handle <YieldTermStructure> discountCurve =
new Handle <YieldTermStructure>(new FlatForward(today, new Handle <Quote>(rate), dayCounter));
IPricingEngine engine = new BinomialConvertibleEngine <JarrowRudd>(stochasticProcess, timeSteps);
ConvertibleFixedCouponBond europeanBond = new ConvertibleFixedCouponBond(exercise, conversionRatio,
dividends, callability, creditSpread, issueDate, settlementDays, coupons, bondDayCount, schedule,
redemption);
europeanBond.setPricingEngine(engine);
ConvertibleFixedCouponBond americanBond = new ConvertibleFixedCouponBond(amexercise, conversionRatio,
dividends, callability, creditSpread, issueDate, settlementDays, coupons, bondDayCount, schedule,
redemption);
americanBond.setPricingEngine(engine);
Console.WriteLine("Jarrow-Rudd {0:0.000000} {1:0.000000}", europeanBond.NPV(), americanBond.NPV());
americanBond.setPricingEngine(new BinomialConvertibleEngine <CoxRossRubinstein>(stochasticProcess, timeSteps));
europeanBond.setPricingEngine(new BinomialConvertibleEngine <CoxRossRubinstein>(stochasticProcess, timeSteps));
Console.WriteLine("CoxRossRubinstein {0:0.000000} {1:0.000000}", europeanBond.NPV(), americanBond.NPV());
americanBond.setPricingEngine(new BinomialConvertibleEngine <AdditiveEQPBinomialTree>(stochasticProcess, timeSteps));
europeanBond.setPricingEngine(new BinomialConvertibleEngine <AdditiveEQPBinomialTree>(stochasticProcess, timeSteps));
Console.WriteLine("AdditiveEQPBinomialTree {0:0.000000} {1:0.000000}", europeanBond.NPV(), americanBond.NPV());
americanBond.setPricingEngine(new BinomialConvertibleEngine <Trigeorgis>(stochasticProcess, timeSteps));
europeanBond.setPricingEngine(new BinomialConvertibleEngine <Trigeorgis>(stochasticProcess, timeSteps));
Console.WriteLine("Trigeorgis {0:0.000000} {1:0.000000}", europeanBond.NPV(), americanBond.NPV());
americanBond.setPricingEngine(new BinomialConvertibleEngine <Tian>(stochasticProcess, timeSteps));
europeanBond.setPricingEngine(new BinomialConvertibleEngine <Tian>(stochasticProcess, timeSteps));
Console.WriteLine("Tian {0:0.000000} {1:0.000000}", europeanBond.NPV(), americanBond.NPV());
americanBond.setPricingEngine(new BinomialConvertibleEngine <LeisenReimer>(stochasticProcess, timeSteps));
europeanBond.setPricingEngine(new BinomialConvertibleEngine <LeisenReimer>(stochasticProcess, timeSteps));
Console.WriteLine("LeisenReimer {0:0.000000} {1:0.000000}", europeanBond.NPV(), americanBond.NPV());
americanBond.setPricingEngine(new BinomialConvertibleEngine <Joshi4>(stochasticProcess, timeSteps));
europeanBond.setPricingEngine(new BinomialConvertibleEngine <Joshi4>(stochasticProcess, timeSteps));
Console.WriteLine("Joshi4 {0:0.000000} {1:0.000000}", europeanBond.NPV(), americanBond.NPV());
Console.WriteLine("===========================================================================");
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
}
catch (Exception e)
{
Console.WriteLine(e.ToString());
}
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
