public void testFdmHestonBlackScholes()
{
//Testing FDM Heston with Black Scholes model...
using (SavedSettings backup = new SavedSettings())
{
Settings.Instance.setEvaluationDate(new Date(28, 3, 2004));
Date exerciseDate = new Date(26, 6, 2004);
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.10, new Actual360()));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.0, new Actual360()));
Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(rTS.currentLink().referenceDate(), 0.25, rTS.currentLink().dayCounter()));
Exercise exercise = new EuropeanExercise(exerciseDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, 10);
VanillaOption option = new VanillaOption(payoff, exercise);
double[] strikes = new double[] { 8, 9, 10, 11, 12 };
double tol = 0.0001;
for (int i = 0; i < strikes.Length; ++i)
{
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(strikes[i]));
GeneralizedBlackScholesProcess bsProcess = new GeneralizedBlackScholesProcess(s0, qTS, rTS, volTS);
option.setPricingEngine(new AnalyticEuropeanEngine(bsProcess));
double expected = option.NPV();
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, s0, 0.0625, 1, 0.0625, 0.0001, 0.0);
// Hundsdorfer scheme
option.setPricingEngine(new FdHestonVanillaEngine(new HestonModel(hestonProcess),
100, 400, 3));
double calculated = option.NPV();
if (Math.Abs(calculated - expected) > tol)
{
QAssert.Fail("Failed to reproduce expected npv"
+ "\n strike: " + strikes[i]
+ "\n calculated: " + calculated
+ "\n expected: " + expected
+ "\n tolerance: " + tol);
}
// Explicit scheme
option.setPricingEngine(new FdHestonVanillaEngine(new HestonModel(hestonProcess),
4000, 400, 3, 0,
new FdmSchemeDesc().ExplicitEuler()));
calculated = option.NPV();
if (Math.Abs(calculated - expected) > tol)
{
QAssert.Fail("Failed to reproduce expected npv"
+ "\n strike: " + strikes[i]
+ "\n calculated: " + calculated
+ "\n expected: " + expected
+ "\n tolerance: " + tol);
}
}
}
}
public void testFdmHestonAmerican()
{
//Testing FDM with American option in Heston model...
using (SavedSettings backup = new SavedSettings())
{
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(100.0));
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.05, new Actual365Fixed()));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.0, new Actual365Fixed()));
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, s0, 0.04, 2.5, 0.04, 0.66, -0.8);
Settings.Instance.setEvaluationDate(new Date(28, 3, 2004));
Date exerciseDate = new Date(28, 3, 2005);
Exercise exercise = new AmericanExercise(exerciseDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, 100);
VanillaOption option = new VanillaOption(payoff, exercise);
IPricingEngine engine = new FdHestonVanillaEngine(new HestonModel(hestonProcess), 200, 100, 50);
option.setPricingEngine(engine);
double tol = 0.01;
double npvExpected = 5.66032;
double deltaExpected = -0.30065;
double gammaExpected = 0.02202;
if (Math.Abs(option.NPV() - npvExpected) > tol)
{
QAssert.Fail("Failed to reproduce expected npv"
+ "\n calculated: " + option.NPV()
+ "\n expected: " + npvExpected
+ "\n tolerance: " + tol);
}
if (Math.Abs(option.delta() - deltaExpected) > tol)
{
QAssert.Fail("Failed to reproduce expected delta"
+ "\n calculated: " + option.delta()
+ "\n expected: " + deltaExpected
+ "\n tolerance: " + tol);
}
if (Math.Abs(option.gamma() - gammaExpected) > tol)
{
QAssert.Fail("Failed to reproduce expected gamma"
+ "\n calculated: " + option.gamma()
+ "\n expected: " + gammaExpected
+ "\n tolerance: " + tol);
}
}
}
public void testOption()
{
/* a zero-coupon convertible bond with no credit spread is
* equivalent to a call option. */
// Testing zero-coupon convertible bonds against vanilla option
CommonVars vars = new CommonVars();
Exercise euExercise = new EuropeanExercise(vars.maturityDate);
vars.settlementDays = 0;
int timeSteps = 2001;
IPricingEngine engine = new BinomialConvertibleEngine <CoxRossRubinstein>(vars.process, timeSteps);
IPricingEngine vanillaEngine = new BinomialVanillaEngine <CoxRossRubinstein>(vars.process, timeSteps);
vars.creditSpread.linkTo(new SimpleQuote(0.0));
double conversionStrike = vars.redemption / vars.conversionRatio;
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Call, conversionStrike);
Schedule schedule = new MakeSchedule().from(vars.issueDate)
.to(vars.maturityDate)
.withFrequency(Frequency.Once)
.withCalendar(vars.calendar)
.backwards().value();
ConvertibleZeroCouponBond euZero = new ConvertibleZeroCouponBond(euExercise, vars.conversionRatio,
vars.no_dividends, vars.no_callability,
vars.creditSpread,
vars.issueDate, vars.settlementDays,
vars.dayCounter, schedule,
vars.redemption);
euZero.setPricingEngine(engine);
VanillaOption euOption = new VanillaOption(payoff, euExercise);
euOption.setPricingEngine(vanillaEngine);
double tolerance = 5.0e-2 * (vars.faceAmount / 100.0);
double expected = vars.faceAmount / 100.0 *
(vars.redemption * vars.riskFreeRate.link.discount(vars.maturityDate)
+ vars.conversionRatio * euOption.NPV());
double error = Math.Abs(euZero.NPV() - expected);
if (error > tolerance)
{
QAssert.Fail("failed to reproduce plain-option price:"
+ "\n calculated: " + euZero.NPV()
+ "\n expected: " + expected
+ "\n error: " + error
+ "\n tolerance: " + tolerance);
}
}
public void testBjerksundStenslandValues()
{
// ("Testing Bjerksund and Stensland approximation for American options...");
AmericanOptionData[] values = new AmericanOptionData[] {
// type, strike, spot, q, r, t, vol, value, tol
// from "Option pricing formulas", Haug, McGraw-Hill 1998, pag 27
new AmericanOptionData(Option.Type.Call, 40.00, 42.00, 0.08, 0.04, 0.75, 0.35, 5.2704),
// from "Option pricing formulas", Haug, McGraw-Hill 1998, VBA code
new AmericanOptionData(Option.Type.Put, 40.00, 36.00, 0.00, 0.06, 1.00, 0.20, 4.4531)
};
Date today = Date.Today;
DayCounter dc = new Actual360();
SimpleQuote spot = new SimpleQuote(0.0);
SimpleQuote qRate = new SimpleQuote(0.0);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.0);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.0);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
double tolerance = 3.0e-3;
for (int i = 0; i < values.Length; i++)
{
StrikedTypePayoff payoff = new PlainVanillaPayoff(values[i].type, values[i].strike);
Date exDate = today + Convert.ToInt32(values[i].t * 360 + 0.5);
Exercise exercise = new AmericanExercise(today, exDate);
spot.setValue(values[i].s);
qRate.setValue(values[i].q);
rRate.setValue(values[i].r);
vol.setValue(values[i].v);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine = new BjerksundStenslandApproximationEngine(stochProcess);
VanillaOption option = new VanillaOption(payoff, exercise);
option.setPricingEngine(engine);
double calculated = option.NPV();
double error = Math.Abs(calculated - values[i].result);
if (error > tolerance)
{
REPORT_FAILURE("value", payoff, exercise, values[i].s, values[i].q,
values[i].r, today, values[i].v, values[i].result,
calculated, error, tolerance);
}
}
}
public void testCashOrNothingEuropeanValues()
{
// Testing European cash-or-nothing digital option
DigitalOptionData[] values =
{
// "Option pricing formulas", E.G. Haug, McGraw-Hill 1998 - pag 88
// type, strike, spot, q, r, t, vol, value, tol
new DigitalOptionData(Option.Type.Put, 80.00, 100.0, 0.06, 0.06, 0.75, 0.35, 2.6710, 1e-4, true)
};
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(0.0);
SimpleQuote qRate = new SimpleQuote(0.0);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.0);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.0);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
for (int i = 0; i < values.Length; i++)
{
StrikedTypePayoff payoff = new CashOrNothingPayoff(values[i].type, values[i].strike, 10.0);
Date exDate = today + Convert.ToInt32(values[i].t * 360 + 0.5);
Exercise exercise = new EuropeanExercise(exDate);
spot.setValue(values[i].s);
qRate.setValue(values[i].q);
rRate.setValue(values[i].r);
vol.setValue(values[i].v);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine = new AnalyticEuropeanEngine(stochProcess);
VanillaOption opt = new VanillaOption(payoff, exercise);
opt.setPricingEngine(engine);
double calculated = opt.NPV();
double error = Math.Abs(calculated - values[i].result);
if (error > values[i].tol)
{
REPORT_FAILURE("value", payoff, exercise, values[i].s, values[i].q,
values[i].r, today, values[i].v, values[i].result,
calculated, error, values[i].tol, values[i].knockin);
}
}
}
// Methods
public double NPV(DateTime pricingDate, IPricingEngine engine)
{
// Set the pricing date
_pricingDate = pricingDate;
Settings.setEvaluationDate(pricingDate);
// Set the pricing engine
_option.setPricingEngine(engine);
_price_points = _option.NPV();
_price_relative = _price_points / _spotAtStrike;
return(_price_relative);
}
public void testFdValues()
{
//("Testing finite-difference engine for American options...");
Date today = Date.Today;
DayCounter dc = new Actual360();
SimpleQuote spot = new SimpleQuote(0.0);
SimpleQuote qRate = new SimpleQuote(0.0);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.0);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.0);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
double tolerance = 8.0e-2;
for (int i = 0; i < juValues.Length; i++)
{
StrikedTypePayoff payoff = new PlainVanillaPayoff(juValues[i].type, juValues[i].strike);
Date exDate = today + Convert.ToInt32(juValues[i].t * 360 + 0.5);
Exercise exercise = new AmericanExercise(today, exDate);
spot.setValue(juValues[i].s);
qRate.setValue(juValues[i].q);
rRate.setValue(juValues[i].r);
vol.setValue(juValues[i].v);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine = new FDAmericanEngine(stochProcess, 100, 100);
VanillaOption option = new VanillaOption(payoff, exercise);
option.setPricingEngine(engine);
double calculated = option.NPV();
double error = Math.Abs(calculated - juValues[i].result);
if (error > tolerance)
{
REPORT_FAILURE("value", payoff, exercise, juValues[i].s, juValues[i].q,
juValues[i].r, today, juValues[i].v, juValues[i].result,
calculated, error, tolerance);
}
}
}
public void testFdmHestonIkonenToivanen()
{
//Testing FDM Heston for Ikonen and Toivanen tests...
/* check prices of american puts as given in:
* From Efficient numerical methods for pricing American options under
* stochastic volatility, Samuli Ikonen, Jari Toivanen,
* http://users.jyu.fi/~tene/papers/reportB12-05.pdf
*/
using (SavedSettings backup = new SavedSettings())
{
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.10, new Actual360()));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.0, new Actual360()));
Settings.Instance.setEvaluationDate(new Date(28, 3, 2004));
Date exerciseDate = new Date(26, 6, 2004);
Exercise exercise = new AmericanExercise(exerciseDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, 10);
VanillaOption option = new VanillaOption(payoff, exercise);
double[] strikes = new double[] { 8, 9, 10, 11, 12 };
double[] expected = new double[] { 2.00000, 1.10763, 0.520038, 0.213681, 0.082046 };
double tol = 0.001;
for (int i = 0; i < strikes.Length; ++i)
{
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(strikes[i]));
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, s0, 0.0625, 5, 0.16, 0.9, 0.1);
IPricingEngine engine = new FdHestonVanillaEngine(new HestonModel(hestonProcess), 100, 400);
option.setPricingEngine(engine);
double calculated = option.NPV();
if (Math.Abs(calculated - expected[i]) > tol)
{
QAssert.Fail("Failed to reproduce expected npv"
+ "\n strike: " + strikes[i]
+ "\n calculated: " + calculated
+ "\n expected: " + expected[i]
+ "\n tolerance: " + tol);
}
}
}
}
/// <summary>
/// Runs option evaluation and logs exceptions
/// </summary>
/// <param name="option"></param>
/// <returns></returns>
private static double EvaluateOption(VanillaOption option)
{
try
{
var npv = option.NPV();
if (double.IsNaN(npv) ||
double.IsInfinity(npv))
{
npv = 0.0;
}
return(npv);
}
catch (Exception err)
{
Log.Debug("QLOptionPriceModel.EvaluateOption() error: " + err.Message);
return(0.0);
}
}
public void testEuropeanStartLimit()
{
// Testing dividend European option with a dividend on today's date...
SavedSettings backup = new SavedSettings();
double tolerance = 1.0e-5;
double dividendValue = 10.0;
Option.Type[] types = { Option.Type.Call, Option.Type.Put };
double[] strikes = { 50.0, 99.5, 100.0, 100.5, 150.0 };
double[] underlyings = { 100.0 };
double[] qRates = { 0.00, 0.10, 0.30 };
double[] rRates = { 0.01, 0.05, 0.15 };
int[] lengths = { 1, 2 };
double[] vols = { 0.05, 0.20, 0.70 };
DayCounter dc = new Actual360();
Date today = Date.Today;
Settings.setEvaluationDate(today);
SimpleQuote spot = 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));
for (int i = 0; i < types.Length; i++)
{
for (int j = 0; j < strikes.Length; j++)
{
for (int k = 0; k < lengths.Length; k++)
{
Date exDate = today + new Period(lengths[k], TimeUnit.Years);
Exercise exercise = new EuropeanExercise(exDate);
List <Date> dividendDates = new List <Date>();
List <double> dividends = new List <double>();
dividendDates.Add(today);
dividends.Add(dividendValue);
StrikedTypePayoff payoff = new PlainVanillaPayoff(types[i], strikes[j]);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot),
qTS, rTS, volTS);
IPricingEngine engine = new AnalyticDividendEuropeanEngine(stochProcess);
IPricingEngine ref_engine = new AnalyticEuropeanEngine(stochProcess);
DividendVanillaOption option = new DividendVanillaOption(payoff, exercise, dividendDates, dividends);
option.setPricingEngine(engine);
VanillaOption ref_option = new VanillaOption(payoff, exercise);
ref_option.setPricingEngine(ref_engine);
for (int l = 0; l < underlyings.Length; l++)
{
for (int m = 0; m < qRates.Length; m++)
{
for (int n = 0; n < rRates.Length; n++)
{
for (int p = 0; p < vols.Length; p++)
{
double u = underlyings[l];
double q = qRates[m],
r = rRates[n];
double v = vols[p];
spot.setValue(u);
qRate.setValue(q);
rRate.setValue(r);
vol.setValue(v);
double calculated = option.NPV();
spot.setValue(u - dividendValue);
double expected = ref_option.NPV();
double error = Math.Abs(calculated - expected);
if (error > tolerance)
{
REPORT_FAILURE("value", payoff, exercise,
u, q, r, today, v,
expected, calculated,
error, tolerance);
}
}
}
}
}
}
}
}
}
public static object eqInstGetOptionGreeks(
[ExcelArgument(Description = "id of option ")] string ObjectId,
[ExcelArgument(Description = "Greek type ")] string gtype,
[ExcelArgument(Description = "Option type (VANILLA or MULTIASSET)")] string otype,
[ExcelArgument(Description = "trigger ")] object trigger)
{
if (ExcelUtil.CallFromWizard())
{
return("");
}
string callerAddress = "";
callerAddress = ExcelUtil.getActiveCellAddress();
try
{
Xl.Range rng = ExcelUtil.getActiveCellRange();
if (ExcelUtil.isNull(gtype))
{
gtype = "NPV";
}
if (ExcelUtil.isNull(otype))
{
otype = "VANILLA";
}
if (otype == "VANILLA")
{
VanillaOption option = OHRepository.Instance.getObject <VanillaOption>(ObjectId);
switch (gtype.ToUpper())
{
case "NPV":
return(option.NPV());
case "DELTA":
return(option.delta());
case "GAMMA":
return(option.gamma());
case "VEGA":
return(option.vega());
case "THETA":
return(option.theta());
case "RHO":
return(option.rho());
default:
return(0);
}
}
else if (otype == "MULTIASSET")
{
BasketOption option = OHRepository.Instance.getObject <BasketOption>(ObjectId);
switch (gtype.ToUpper())
{
case "NPV":
return(option.NPV());
case "DELTA":
return(option.delta());
case "GAMMA":
return(option.gamma());
case "VEGA":
return(option.vega());
case "THETA":
return(option.theta());
case "RHO":
return(option.rho());
default:
return(0);
}
}
else
{
return("Unknown option type");
}
}
catch (Exception e)
{
ExcelUtil.logError(callerAddress, System.Reflection.MethodInfo.GetCurrentMethod().Name.ToString(), e.Message);
return("#EQ_ERR!");
}
}
public void testCrankNicolsonWithDamping()
{
SavedSettings backup = new SavedSettings();
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(100.0);
YieldTermStructure qTS = Utilities.flatRate(today, 0.06, dc);
YieldTermStructure rTS = Utilities.flatRate(today, 0.06, dc);
BlackVolTermStructure volTS = Utilities.flatVol(today, 0.35, dc);
StrikedTypePayoff payoff =
new CashOrNothingPayoff(Option.Type.Put, 100, 10.0);
double maturity = 0.75;
Date exDate = today + Convert.ToInt32(maturity * 360 + 0.5);
Exercise exercise = new EuropeanExercise(exDate);
BlackScholesMertonProcess process = new
BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine =
new AnalyticEuropeanEngine(process);
VanillaOption opt = new VanillaOption(payoff, exercise);
opt.setPricingEngine(engine);
double expectedPV = opt.NPV();
double expectedGamma = opt.gamma();
// fd pricing using implicit damping steps and Crank Nicolson
int csSteps = 25, dampingSteps = 3, xGrid = 400;
List <int> dim = new InitializedList <int>(1, xGrid);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(
dim[0], process, maturity, payoff.strike(),
null, null, 0.0001, 1.5,
new Pair <double?, double?>(payoff.strike(), 0.01));
FdmMesher mesher =
new FdmMesherComposite(equityMesher);
FdmBlackScholesOp map =
new FdmBlackScholesOp(mesher, process, payoff.strike());
FdmInnerValueCalculator calculator =
new FdmLogInnerValue(payoff, mesher, 0);
object rhs = new Vector(layout.size());
Vector x = new Vector(layout.size());
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter;
++iter)
{
(rhs as Vector)[iter.index()] = calculator.avgInnerValue(iter, maturity);
x[iter.index()] = mesher.location(iter, 0);
}
FdmBackwardSolver solver = new FdmBackwardSolver(map, new FdmBoundaryConditionSet(),
new FdmStepConditionComposite(),
new FdmSchemeDesc().Douglas());
solver.rollback(ref rhs, maturity, 0.0, csSteps, dampingSteps);
MonotonicCubicNaturalSpline spline = new MonotonicCubicNaturalSpline(x, x.Count, rhs as Vector);
double s = spot.value();
double calculatedPV = spline.value(Math.Log(s));
double calculatedGamma = (spline.secondDerivative(Math.Log(s))
- spline.derivative(Math.Log(s))) / (s * s);
double relTol = 2e-3;
if (Math.Abs(calculatedPV - expectedPV) > relTol * expectedPV)
{
QAssert.Fail("Error calculating the PV of the digital option" +
"\n rel. tolerance: " + relTol +
"\n expected: " + expectedPV +
"\n calculated: " + calculatedPV);
}
if (Math.Abs(calculatedGamma - expectedGamma) > relTol * expectedGamma)
{
QAssert.Fail("Error calculating the Gamma of the digital option" +
"\n rel. tolerance: " + relTol +
"\n expected: " + expectedGamma +
"\n calculated: " + calculatedGamma);
}
}
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);
}
public void testAssetAtExpiryOrNothingAmericanValues()
{
// Testing American asset-(at-expiry)-or-nothing digital option
DigitalOptionData[] values =
{
// type, strike, spot, q, r, t, vol, value, tol
// "Option pricing formulas", E.G. Haug, McGraw-Hill 1998 - pag 95, case 7,8,11,12
new DigitalOptionData(Option.Type.Put, 100.00, 105.00, 0.00, 0.10, 0.5, 0.20, 64.8426, 1e-04, true),
new DigitalOptionData(Option.Type.Call, 100.00, 95.00, 0.00, 0.10, 0.5, 0.20, 77.7017, 1e-04, true),
new DigitalOptionData(Option.Type.Put, 100.00, 105.00, 0.00, 0.10, 0.5, 0.20, 40.1574, 1e-04, false),
new DigitalOptionData(Option.Type.Call, 100.00, 95.00, 0.00, 0.10, 0.5, 0.20, 17.2983, 1e-04, false),
// data from Haug VBA code results
new DigitalOptionData(Option.Type.Put, 100.00, 105.00, 0.01, 0.10, 0.5, 0.20, 65.5291, 1e-04, true),
new DigitalOptionData(Option.Type.Call, 100.00, 95.00, 0.01, 0.10, 0.5, 0.20, 76.5951, 1e-04, true),
// in the money options (guaranteed discounted payoff = forward * riskFreeDiscount
// = spot * dividendDiscount)
new DigitalOptionData(Option.Type.Call, 100.00, 105.00, 0.00, 0.10, 0.5, 0.20, 105.0000, 1e-12, true),
new DigitalOptionData(Option.Type.Put, 100.00, 95.00, 0.00, 0.10, 0.5, 0.20, 95.0000, 1e-12, true),
new DigitalOptionData(Option.Type.Call, 100.00, 105.00, 0.01, 0.10, 0.5, 0.20, 105.0000 * Math.Exp(-0.005), 1e-12, true),
new DigitalOptionData(Option.Type.Put, 100.00, 95.00, 0.01, 0.10, 0.5, 0.20, 95.0000 * Math.Exp(-0.005), 1e-12, true)
};
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(100.0);
SimpleQuote qRate = new SimpleQuote(0.04);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.01);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.25);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
for (int i = 0; i < values.Length; i++)
{
StrikedTypePayoff payoff = new AssetOrNothingPayoff(values[i].type, values[i].strike);
Date exDate = today + Convert.ToInt32(values[i].t * 360 + 0.5);
Exercise amExercise = new AmericanExercise(today, exDate, true);
spot.setValue(values[i].s);
qRate.setValue(values[i].q);
rRate.setValue(values[i].r);
vol.setValue(values[i].v);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine;
if (values[i].knockin)
{
engine = new AnalyticDigitalAmericanEngine(stochProcess);
}
else
{
engine = new AnalyticDigitalAmericanKOEngine(stochProcess);
}
VanillaOption opt = new VanillaOption(payoff, amExercise);
opt.setPricingEngine(engine);
double calculated = opt.NPV();
double error = Math.Abs(calculated - values[i].result);
if (error > values[i].tol)
{
REPORT_FAILURE("value", payoff, amExercise, values[i].s,
values[i].q, values[i].r, today, values[i].v,
values[i].result, calculated, error, values[i].tol, values[i].knockin);
}
}
}
public void testCashAtHitOrNothingAmericanValues()
{
// Testing American cash-(at-hit)-or-nothing digital option
DigitalOptionData[] values =
{
// type, strike, spot, q, r, t, vol, value, tol
// "Option pricing formulas", E.G. Haug, McGraw-Hill 1998 - pag 95, case 1,2
new DigitalOptionData(Option.Type.Put, 100.00, 105.00, 0.00, 0.10, 0.5, 0.20, 9.7264, 1e-4, true),
new DigitalOptionData(Option.Type.Call, 100.00, 95.00, 0.00, 0.10, 0.5, 0.20, 11.6553, 1e-4, true),
// the following cases are not taken from a reference paper or book
// in the money options (guaranteed immediate payoff)
new DigitalOptionData(Option.Type.Call, 100.00, 105.00, 0.00, 0.10, 0.5, 0.20, 15.0000, 1e-16, true),
new DigitalOptionData(Option.Type.Put, 100.00, 95.00, 0.00, 0.10, 0.5, 0.20, 15.0000, 1e-16, true),
// non null dividend (cross-tested with MC simulation)
new DigitalOptionData(Option.Type.Put, 100.00, 105.00, 0.20, 0.10, 0.5, 0.20, 12.2715, 1e-4, true),
new DigitalOptionData(Option.Type.Call, 100.00, 95.00, 0.20, 0.10, 0.5, 0.20, 8.9109, 1e-4, true),
new DigitalOptionData(Option.Type.Call, 100.00, 105.00, 0.20, 0.10, 0.5, 0.20, 15.0000, 1e-16, true),
new DigitalOptionData(Option.Type.Put, 100.00, 95.00, 0.20, 0.10, 0.5, 0.20, 15.0000, 1e-16, true)
};
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(0.0);
SimpleQuote qRate = new SimpleQuote(0.0);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.0);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.0);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
for (int i = 0; i < values.Length; i++)
{
StrikedTypePayoff payoff = new CashOrNothingPayoff(values[i].type, values[i].strike, 15.00);
Date exDate = today + Convert.ToInt32(values[i].t * 360 + 0.5);
Exercise amExercise = new AmericanExercise(today, exDate);
spot.setValue(values[i].s);
qRate.setValue(values[i].q);
rRate.setValue(values[i].r);
vol.setValue(values[i].v);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine = new AnalyticDigitalAmericanEngine(stochProcess);
VanillaOption opt = new VanillaOption(payoff, amExercise);
opt.setPricingEngine(engine);
double calculated = opt.NPV();
double error = Math.Abs(calculated - values[i].result);
if (error > values[i].tol)
{
REPORT_FAILURE("value", payoff, amExercise, values[i].s,
values[i].q, values[i].r, today, values[i].v,
values[i].result, calculated, error, values[i].tol, values[i].knockin);
}
}
}
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();
}
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 testFdmHestonConvergence()
{
/* convergence tests based on
* ADI finite difference schemes for option pricing in the
* Heston model with correlation, K.J. in t'Hout and S. Foulon
*/
//Testing FDM Heston convergence...
using (SavedSettings backup = new SavedSettings())
{
HestonTestData[] values = new HestonTestData[] {
new HestonTestData(1.5, 0.04, 0.3, -0.9, 0.025, 0.0, 1.0, 100),
new HestonTestData(3.0, 0.12, 0.04, 0.6, 0.01, 0.04, 1.0, 100),
new HestonTestData(0.6067, 0.0707, 0.2928, -0.7571, 0.03, 0.0, 3.0, 100),
new HestonTestData(2.5, 0.06, 0.5, -0.1, 0.0507, 0.0469, 0.25, 100)
};
FdmSchemeDesc[] schemes = new FdmSchemeDesc[] {
new FdmSchemeDesc().Hundsdorfer(),
new FdmSchemeDesc().ModifiedCraigSneyd(),
new FdmSchemeDesc().ModifiedHundsdorfer(),
new FdmSchemeDesc().CraigSneyd(),
new FdmSchemeDesc().TrBDF2(),
new FdmSchemeDesc().CrankNicolson(),
};
int[] tn = new int[] { 60 };
double[] v0 = new double[] { 0.04 };
Date todaysDate = new Date(28, 3, 2004);
Settings.Instance.setEvaluationDate(todaysDate);
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(75.0));
for (int l = 0; l < schemes.Length; ++l)
{
for (int i = 0; i < values.Length; ++i)
{
for (int j = 0; j < tn.Length; ++j)
{
for (int k = 0; k < v0.Length; ++k)
{
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(
Utilities.flatRate(values[i].r, new Actual365Fixed()));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(
Utilities.flatRate(values[i].q, new Actual365Fixed()));
HestonProcess hestonProcess =
new HestonProcess(rTS, qTS, s0,
v0[k],
values[i].kappa,
values[i].theta,
values[i].sigma,
values[i].rho);
Date exerciseDate = todaysDate
+ new Period(Convert.ToInt32(values[i].T * 365), TimeUnit.Days);
Exercise exercise = new EuropeanExercise(exerciseDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Call, values[i].K);
VanillaOption option = new VanillaOption(payoff, exercise);
IPricingEngine engine =
new FdHestonVanillaEngine(
new HestonModel(hestonProcess),
tn[j], 101, 51, 0,
schemes[l]);
option.setPricingEngine(engine);
double calculated = option.NPV();
IPricingEngine analyticEngine =
new AnalyticHestonEngine(
new HestonModel(hestonProcess), 144);
option.setPricingEngine(analyticEngine);
double expected = option.NPV();
if (Math.Abs(expected - calculated) / expected > 0.02 &&
Math.Abs(expected - calculated) > 0.002)
{
QAssert.Fail("Failed to reproduce expected npv"
+ "\n calculated: " + calculated
+ "\n expected: " + expected
+ "\n tolerance: " + 0.01);
}
}
}
}
}
}
}
public void testBaroneAdesiWhaleyValues()
{
// ("Testing Barone-Adesi and Whaley approximation for American options...");
/* The data below are from
* "Option pricing formulas", E.G. Haug, McGraw-Hill 1998 pag 24
*
* The following values were replicated only up to the second digit
* by the VB code provided by Haug, which was used as base for the
* C++ implementation
*
*/
AmericanOptionData[] values =
{
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.15, 0.0206),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.15, 1.8771),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.15, 10.0089),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.25, 0.3159),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.25, 3.1280),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.25, 10.3919),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.10, 0.35, 0.9495),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.35, 4.3777),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.35, 11.1679),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.15, 0.8208),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.15, 4.0842),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.15, 10.8087),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.25, 2.7437),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.25, 6.8015),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.25, 13.0170),
new AmericanOptionData(Option.Type.Call, 100.00, 90.00, 0.10, 0.10, 0.50, 0.35, 5.0063),
new AmericanOptionData(Option.Type.Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.35, 9.5106),
new AmericanOptionData(Option.Type.Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.35, 15.5689),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.15, 10.0000),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.15, 1.8770),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.15, 0.0410),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.25, 10.2533),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.25, 3.1277),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.25, 0.4562),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.10, 0.35, 10.8787),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.10, 0.35, 4.3777),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.10, 0.35, 1.2402),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.15, 10.5595),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.15, 4.0842),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.15, 1.0822),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.25, 12.4419),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.25, 6.8014),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.25, 3.3226),
new AmericanOptionData(Option.Type.Put, 100.00, 90.00, 0.10, 0.10, 0.50, 0.35, 14.6945),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.10, 0.10, 0.50, 0.35, 9.5104),
new AmericanOptionData(Option.Type.Put, 100.00, 110.00, 0.10, 0.10, 0.50, 0.35, 5.8823),
new AmericanOptionData(Option.Type.Put, 100.00, 100.00, 0.00, 0.00, 0.50, 0.15, 4.22949)
};
Date today = Date.Today;
DayCounter dc = new Actual360();
SimpleQuote spot = new SimpleQuote(0.0);
SimpleQuote qRate = new SimpleQuote(0.0);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.0);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.0);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
double tolerance = 3.0e-3;
for (int i = 0; i < values.Length; i++)
{
StrikedTypePayoff payoff = new PlainVanillaPayoff(values[i].type, values[i].strike);
Date exDate = today + Convert.ToInt32(values[i].t * 360 + 0.5);
Exercise exercise = new AmericanExercise(today, exDate);
spot.setValue(values[i].s);
qRate.setValue(values[i].q);
rRate.setValue(values[i].r);
vol.setValue(values[i].v);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine = new BaroneAdesiWhaleyApproximationEngine(stochProcess);
VanillaOption option = new VanillaOption(payoff, exercise);
option.setPricingEngine(engine);
double calculated = option.NPV();
double error = Math.Abs(calculated - values[i].result);
if (error > tolerance)
{
REPORT_FAILURE("value", payoff, exercise, values[i].s, values[i].q,
values[i].r, today, values[i].v, values[i].result,
calculated, error, tolerance);
}
}
}
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 testFdGreeks <Engine>() where Engine : IFDEngine, new()
{
using (SavedSettings backup = new SavedSettings())
{
Dictionary <string, double> calculated = new Dictionary <string, double>(),
expected = new Dictionary <string, double>(),
tolerance = new Dictionary <string, double>();
tolerance.Add("delta", 7.0e-4);
tolerance.Add("gamma", 2.0e-4);
//tolerance["theta"] = 1.0e-4;
Option.Type[] types = new Option.Type[] { Option.Type.Call, Option.Type.Put };
double[] strikes = { 50.0, 99.5, 100.0, 100.5, 150.0 };
double[] underlyings = { 100.0 };
double[] qRates = { 0.04, 0.05, 0.06 };
double[] rRates = { 0.01, 0.05, 0.15 };
int[] years = { 1, 2 };
double[] vols = { 0.11, 0.50, 1.20 };
Date today = Date.Today;
Settings.setEvaluationDate(today);
DayCounter dc = new Actual360();
SimpleQuote spot = new SimpleQuote(0.0);
SimpleQuote qRate = new SimpleQuote(0.0);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.0);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.0);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
for (int i = 0; i < types.Length; i++)
{
for (int j = 0; j < strikes.Length; j++)
{
for (int k = 0; k < years.Length; k++)
{
Date exDate = today + new Period(years[k], TimeUnit.Years);
Exercise exercise = new AmericanExercise(today, exDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(types[i], strikes[j]);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine = new Engine().factory(stochProcess);
VanillaOption option = new VanillaOption(payoff, exercise);
option.setPricingEngine(engine);
for (int l = 0; l < underlyings.Length; l++)
{
for (int m = 0; m < qRates.Length; m++)
{
for (int n = 0; n < rRates.Length; n++)
{
for (int p = 0; p < vols.Length; p++)
{
double u = underlyings[l];
double q = qRates[m],
r = rRates[n];
double v = vols[p];
spot.setValue(u);
qRate.setValue(q);
rRate.setValue(r);
vol.setValue(v);
double value = option.NPV();
calculated.Add("delta", option.delta());
calculated.Add("gamma", option.gamma());
//calculated["theta"] = option.theta();
if (value > spot.value() * 1.0e-5)
{
// perturb spot and get delta and gamma
double du = u * 1.0e-4;
spot.setValue(u + du);
double value_p = option.NPV(),
delta_p = option.delta();
spot.setValue(u - du);
double value_m = option.NPV(),
delta_m = option.delta();
spot.setValue(u);
expected.Add("delta", (value_p - value_m) / (2 * du));
expected.Add("gamma", (delta_p - delta_m) / (2 * du));
/*
* // perturb date and get theta
* Time dT = dc.yearFraction(today-1, today+1);
* Settings::instance().setEvaluationDate(today-1);
* value_m = option.NPV();
* Settings::instance().setEvaluationDate(today+1);
* value_p = option.NPV();
* Settings::instance().setEvaluationDate(today);
* expected["theta"] = (value_p - value_m)/dT;
*/
// compare
foreach (string greek in calculated.Keys)
{
double expct = expected[greek],
calcl = calculated[greek],
tol = tolerance[greek];
double error = Utilities.relativeError(expct, calcl, u);
if (error > tol)
{
REPORT_FAILURE(greek, payoff, exercise,
u, q, r, today, v,
expct, calcl, error, tol);
}
}
}
calculated.Clear();
expected.Clear();
}
}
}
}
}
}
}
}
}
public void testAnalyticHestonHullWhitePricing()
{
// Testing analytic Heston Hull-White option pricing
DayCounter dc = new Actual360();
Date today = Date.Today;
Settings.Instance.setEvaluationDate(today);
// construct a strange yield curve to check drifts and discounting
// of the joint stochastic process
List <Date> dates = new List <Date>();
List <double> times = new List <double>();
List <double> rates = new List <double>(), divRates = new List <double>();
for (int i = 0; i <= 40; ++i)
{
dates.Add(today + new Period(i, TimeUnit.Years));
// FLOATING_POINT_EXCEPTION
rates.Add(0.03 + 0.0001 * Math.Exp(Math.Sin(i / 4.0)));
divRates.Add(0.02 + 0.0002 * Math.Exp(Math.Sin(i / 3.0)));
times.Add(dc.yearFraction(today, dates.Last()));
}
Date maturity = today + new Period(5, TimeUnit.Years);
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(100));
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(new InterpolatedZeroCurve <Linear>(dates, rates, dc));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(new InterpolatedZeroCurve <Linear>(dates, divRates, dc));
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, s0, 0.08, 1.5, 0.0625, 0.5, -0.8);
HestonModel hestonModel = new HestonModel(hestonProcess);
HullWhiteForwardProcess hwFwdProcess = new HullWhiteForwardProcess(rTS, 0.01, 0.01);
hwFwdProcess.setForwardMeasureTime(dc.yearFraction(today, maturity));
HullWhite hullWhiteModel = new HullWhite(rTS, hwFwdProcess.a(), hwFwdProcess.sigma());
double tol = 0.002;
double[] strike = { 80, 120 };
Option.Type[] types = { Option.Type.Put, Option.Type.Call };
for (int i = 0; i < types.Length; ++i)
{
for (int j = 0; j < strike.Length; ++j)
{
HybridHestonHullWhiteProcess jointProcess = new HybridHestonHullWhiteProcess(hestonProcess,
hwFwdProcess, 0.0, HybridHestonHullWhiteProcess.Discretization.Euler);
StrikedTypePayoff payoff = new PlainVanillaPayoff(types[i], strike[j]);
Exercise exercise = new EuropeanExercise(maturity);
VanillaOption optionHestonHW = new VanillaOption(payoff, exercise);
optionHestonHW.setPricingEngine(new MakeMCHestonHullWhiteEngine <PseudoRandom, Statistics>(jointProcess)
.withSteps(1)
.withAntitheticVariate()
.withControlVariate()
.withAbsoluteTolerance(tol)
.withSeed(42).getAsPricingEngine());
VanillaOption optionPureHeston = new VanillaOption(payoff, exercise);
optionPureHeston.setPricingEngine(new AnalyticHestonHullWhiteEngine(hestonModel, hullWhiteModel, 128));
double calculated = optionHestonHW.NPV();
double error = optionHestonHW.errorEstimate();
double expected = optionPureHeston.NPV();
if (Math.Abs(calculated - expected) > 3 * error &&
Math.Abs(calculated - expected) > tol)
{
QAssert.Fail("Failed to reproduce hw heston vanilla prices"
+ "\n strike: " + strike[j]
+ "\n calculated: " + calculated
+ "\n error: " + error
+ "\n expected: " + expected);
}
}
}
}
public void testCashAtExpiryOrNothingAmericanValues()
{
// Testing American cash-(at-expiry)-or-nothing digital option
DigitalOptionData[] values =
{
// type, strike, spot, q, r, t, vol, value, tol
// "Option pricing formulas", E.G. Haug, McGraw-Hill 1998 - pag 95, case 5,6,9,10
new DigitalOptionData(Option.Type.Put, 100.00, 105.00, 0.00, 0.10, 0.5, 0.20, 9.3604, 1e-4, true),
new DigitalOptionData(Option.Type.Call, 100.00, 95.00, 0.00, 0.10, 0.5, 0.20, 11.2223, 1e-4, true),
new DigitalOptionData(Option.Type.Put, 100.00, 105.00, 0.00, 0.10, 0.5, 0.20, 4.9081, 1e-4, false),
new DigitalOptionData(Option.Type.Call, 100.00, 95.00, 0.00, 0.10, 0.5, 0.20, 3.0461, 1e-4, false),
// in the money options (guaranteed discounted payoff)
new DigitalOptionData(Option.Type.Call, 100.00, 105.00, 0.00, 0.10, 0.5, 0.20, 15.0000 * Math.Exp(-0.05), 1e-12, true),
new DigitalOptionData(Option.Type.Put, 100.00, 95.00, 0.00, 0.10, 0.5, 0.20, 15.0000 * Math.Exp(-0.05), 1e-12, true),
// out of bonds case
new DigitalOptionData(Option.Type.Call, 2.37, 2.33, 0.07, 0.43, 0.19, 0.005, 0.0000, 1e-4, false),
};
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(100.0);
SimpleQuote qRate = new SimpleQuote(0.04);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.01);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
SimpleQuote vol = new SimpleQuote(0.25);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
for (int i = 0; i < values.Length; i++)
{
StrikedTypePayoff payoff = new CashOrNothingPayoff(values[i].type, values[i].strike, 15.0);
Date exDate = today + Convert.ToInt32(values[i].t * 360 + 0.5);
Exercise amExercise = new AmericanExercise(today, exDate, true);
spot.setValue(values[i].s);
qRate.setValue(values[i].q);
rRate.setValue(values[i].r);
vol.setValue(values[i].v);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine;
if (values[i].knockin)
{
engine = new AnalyticDigitalAmericanEngine(stochProcess);
}
else
{
engine = new AnalyticDigitalAmericanKOEngine(stochProcess);
}
VanillaOption opt = new VanillaOption(payoff, amExercise);
opt.setPricingEngine(engine);
double calculated = opt.NPV();
double error = Math.Abs(calculated - values[i].result);
if (error > values[i].tol)
{
REPORT_FAILURE("value", payoff, amExercise, values[i].s,
values[i].q, values[i].r, today, values[i].v,
values[i].result, calculated, error, values[i].tol, values[i].knockin);
}
}
}
public void testDiscretizationError()
{
// Testing the discretization error of the Heston Hull-White process
DayCounter dc = new Actual360();
Date today = Date.Today;
Settings.Instance.setEvaluationDate(today);
// construct a strange yield curve to check drifts and discounting
// of the joint stochastic process
List <Date> dates = new List <Date>();
List <double> times = new List <double>();
List <double> rates = new List <double>(), divRates = new List <double>();
for (int i = 0; i <= 31; ++i)
{
dates.Add(today + new Period(i, TimeUnit.Years));
// FLOATING_POINT_EXCEPTION
rates.Add(0.04 + 0.0001 * Math.Exp(Math.Sin(i)));
divRates.Add(0.04 + 0.0001 * Math.Exp(Math.Sin(i)));
times.Add(dc.yearFraction(today, dates.Last()));
}
Date maturity = today + new Period(10, TimeUnit.Years);
double v = 0.25;
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(100));
SimpleQuote vol = new SimpleQuote(v);
Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(today, vol, dc));
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(new InterpolatedZeroCurve <Linear>(dates, rates, dc));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(new InterpolatedZeroCurve <Linear>(dates, divRates, dc));
BlackScholesMertonProcess bsmProcess = new BlackScholesMertonProcess(s0, qTS, rTS, volTS);
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, s0, v * v, 1, v * v, 1e-6, -0.4);
HullWhiteForwardProcess hwProcess = new HullWhiteForwardProcess(rTS, 0.01, 0.01);
hwProcess.setForwardMeasureTime(20.1472222222222222);
double tol = 0.05;
double[] corr = { -0.85, 0.5 };
double[] strike = { 50, 100, 125 };
for (int i = 0; i < corr.Length; ++i)
{
for (int j = 0; j < strike.Length; ++j)
{
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, strike[j]);
Exercise exercise = new EuropeanExercise(maturity);
VanillaOption optionBsmHW = new VanillaOption(payoff, exercise);
HullWhite hwModel = new HullWhite(rTS, hwProcess.a(), hwProcess.sigma());
optionBsmHW.setPricingEngine(new AnalyticBSMHullWhiteEngine(corr[i], bsmProcess, hwModel));
double expected = optionBsmHW.NPV();
VanillaOption optionHestonHW = new VanillaOption(payoff, exercise);
HybridHestonHullWhiteProcess jointProcess = new HybridHestonHullWhiteProcess(hestonProcess,
hwProcess, corr[i]);
optionHestonHW.setPricingEngine(
new MakeMCHestonHullWhiteEngine <PseudoRandom, Statistics>(jointProcess)
.withSteps(1)
.withAntitheticVariate()
.withAbsoluteTolerance(tol)
.withSeed(42).getAsPricingEngine());
double calculated = optionHestonHW.NPV();
double error = optionHestonHW.errorEstimate();
if ((Math.Abs(calculated - expected) > 3 * error &&
Math.Abs(calculated - expected) > 1e-5))
{
QAssert.Fail("Failed to reproduce discretization error"
+ "\n corr: " + corr[i]
+ "\n strike: " + strike[j]
+ "\n calculated: " + calculated
+ "\n error: " + error
+ "\n expected: " + expected);
}
}
}
}
public void testCashAtHitOrNothingAmericanGreeks()
{
// Testing American cash-(at-hit)-or-nothing digital option greeks
SavedSettings backup = new SavedSettings();
SortedDictionary <string, double> calculated = new SortedDictionary <string, double>();
SortedDictionary <string, double> expected = new SortedDictionary <string, double>();
SortedDictionary <string, double> tolerance = new SortedDictionary <string, double>(); // std::map<std::string,Real> calculated, expected, tolerance;
tolerance["delta"] = 5.0e-5;
tolerance["gamma"] = 5.0e-5;
tolerance["rho"] = 5.0e-5;
Option.Type[] types = { QLNet.Option.Type.Call, QLNet.Option.Type.Put };
double[] strikes = { 50.0, 99.5, 100.5, 150.0 };
double cashPayoff = 100.0;
double[] underlyings = { 100 };
double[] qRates = { 0.04, 0.05, 0.06 };
double[] rRates = { 0.01, 0.05, 0.15 };
double[] vols = { 0.11, 0.5, 1.2 };
DayCounter dc = new Actual360();
Date today = Date.Today;
Settings.setEvaluationDate(today);
SimpleQuote spot = 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));
// there is no cycling on different residual times
Date exDate = today + 360;
Exercise exercise = new EuropeanExercise(exDate);
Exercise amExercise = new AmericanExercise(today, exDate, false);
Exercise[] exercises = { exercise, amExercise };
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(new Handle <Quote>(spot), qTS, rTS, volTS);
IPricingEngine euroEngine = new AnalyticEuropeanEngine(stochProcess);
IPricingEngine amEngine = new AnalyticDigitalAmericanEngine(stochProcess);
IPricingEngine[] engines = { euroEngine, amEngine };
bool knockin = true;
for (int j = 0; j < engines.Length; j++)
{
for (int i1 = 0; i1 < types.Length; i1++)
{
for (int i6 = 0; i6 < strikes.Length; i6++)
{
StrikedTypePayoff payoff = new CashOrNothingPayoff(types[i1], strikes[i6], cashPayoff);
VanillaOption opt = new VanillaOption(payoff, exercises[j]);
opt.setPricingEngine(engines[j]);
for (int i2 = 0; i2 < underlyings.Length; i2++)
{
for (int i4 = 0; i4 < qRates.Length; i4++)
{
for (int i3 = 0; i3 < rRates.Length; i3++)
{
for (int i7 = 0; i7 < vols.Length; i7++)
{
// test data
double u = underlyings[i2];
double q = qRates[i4];
double r = rRates[i3];
double v = vols[i7];
spot.setValue(u);
qRate.setValue(q);
rRate.setValue(r);
vol.setValue(v);
// theta, dividend rho and vega are not available for
// digital option with american exercise. Greeks of
// digital options with european payoff are tested
// in the europeanoption.cpp test
double value = opt.NPV();
calculated["delta"] = opt.delta();
calculated["gamma"] = opt.gamma();
calculated["rho"] = opt.rho();
if (value > 1.0e-6)
{
// perturb spot and get delta and gamma
double du = u * 1.0e-4;
spot.setValue(u + du);
double value_p = opt.NPV(),
delta_p = opt.delta();
spot.setValue(u - du);
double value_m = opt.NPV(),
delta_m = opt.delta();
spot.setValue(u);
expected["delta"] = (value_p - value_m) / (2 * du);
expected["gamma"] = (delta_p - delta_m) / (2 * du);
// perturb rates and get rho and dividend rho
double dr = r * 1.0e-4;
rRate.setValue(r + dr);
value_p = opt.NPV();
rRate.setValue(r - dr);
value_m = opt.NPV();
rRate.setValue(r);
expected["rho"] = (value_p - value_m) / (2 * dr);
// check
//std::map<std::string,Real>::iterator it;
foreach (var it in calculated)
{
string greek = it.Key;
double expct = expected [greek],
calcl = calculated[greek],
tol = tolerance [greek];
double error = Utilities.relativeError(expct, calcl, value);
if (error > tol)
{
REPORT_FAILURE(greek, payoff, exercise,
u, q, r, today, v,
expct, calcl, error, tol, knockin);
}
}
}
}
}
}
}
}
}
}
}
public void testH1HWPricingEngine()
{
/*
* Example taken from Lech Aleksander Grzelak,
* Equity and Foreign Exchange Hybrid Models for Pricing Long-Maturity
* Financial Derivatives,
* http://repository.tudelft.nl/assets/uuid:a8e1a007-bd89-481a-aee3-0e22f15ade6b/PhDThesis_main.pdf
*/
Date today = new Date(15, Month.July, 2012);
Settings.Instance.setEvaluationDate(today);
Date exerciseDate = new Date(13, Month.July, 2022);
DayCounter dc = new Actual365Fixed();
Exercise exercise = new EuropeanExercise(exerciseDate);
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(100.0));
double r = 0.02;
double q = 0.00;
double v0 = 0.05;
double theta = 0.05;
double kappa_v = 0.3;
double[] sigma_v = { 0.3, 0.6 };
double rho_sv = -0.30;
double rho_sr = 0.6;
double kappa_r = 0.01;
double sigma_r = 0.01;
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, r, dc));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, q, dc));
Handle <BlackVolTermStructure> flatVolTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(today, 0.20, dc));
GeneralizedBlackScholesProcess bsProcess = new GeneralizedBlackScholesProcess(s0, qTS, rTS, flatVolTS);
HullWhiteProcess hwProcess = new HullWhiteProcess(rTS, kappa_r, sigma_r);
HullWhite hullWhiteModel = new HullWhite(new Handle <YieldTermStructure>(rTS), kappa_r, sigma_r);
double tol = 0.0001;
double[] strikes = { 40, 80, 100, 120, 180 };
double[][] expected =
{
new double[] { 0.267503, 0.235742, 0.228223, 0.223461, 0.217855 },
new double[] { 0.263626, 0.211625, 0.199907, 0.193502, 0.190025 }
};
for (int j = 0; j < sigma_v.Length; ++j)
{
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, s0, v0, kappa_v, theta, sigma_v[j], rho_sv);
HestonModel hestonModel = new HestonModel(hestonProcess);
for (int i = 0; i < strikes.Length; ++i)
{
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Call, strikes[i]);
VanillaOption option = new VanillaOption(payoff, exercise);
IPricingEngine analyticH1HWEngine = new AnalyticH1HWEngine(hestonModel, hullWhiteModel, rho_sr, 144);
option.setPricingEngine(analyticH1HWEngine);
double impliedH1HW = option.impliedVolatility(option.NPV(), bsProcess);
if (Math.Abs(expected[j][i] - impliedH1HW) > tol)
{
QAssert.Fail("Failed to reproduce H1HW implied volatility"
+ "\n expected : " + expected[j][i]
+ "\n calculated : " + impliedH1HW
+ "\n tol : " + tol
+ "\n strike : " + strikes[i]
+ "\n sigma : " + sigma_v[j]);
}
}
}
}
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 BinomialJRVanillaEngine(stochasticProcess, timeSteps));
bermudanOption.setPricingEngine(
new BinomialJRVanillaEngine(stochasticProcess, timeSteps));
americanOption.setPricingEngine(
new BinomialJRVanillaEngine(stochasticProcess, 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 BinomialCRRVanillaEngine(stochasticProcess, timeSteps));
bermudanOption.setPricingEngine(
new BinomialCRRVanillaEngine(stochasticProcess, timeSteps));
americanOption.setPricingEngine(
new BinomialCRRVanillaEngine(stochasticProcess, 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 BinomialEQPVanillaEngine(stochasticProcess, timeSteps));
bermudanOption.setPricingEngine(
new BinomialEQPVanillaEngine(stochasticProcess, timeSteps));
americanOption.setPricingEngine(
new BinomialEQPVanillaEngine(stochasticProcess, timeSteps));
ReportResults("Additive Equiprobabilities",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Trigeorgis
try {
europeanOption.setPricingEngine(
new BinomialTrigeorgisVanillaEngine(stochasticProcess, timeSteps));
bermudanOption.setPricingEngine(
new BinomialTrigeorgisVanillaEngine(stochasticProcess, timeSteps));
americanOption.setPricingEngine(
new BinomialTrigeorgisVanillaEngine(stochasticProcess, timeSteps));
ReportResults("Binomial Trigeorgis",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Tian
try {
europeanOption.setPricingEngine(
new BinomialTianVanillaEngine(stochasticProcess, timeSteps));
bermudanOption.setPricingEngine(
new BinomialTianVanillaEngine(stochasticProcess, timeSteps));
americanOption.setPricingEngine(
new BinomialTianVanillaEngine(stochasticProcess, timeSteps));
ReportResults("Binomial Tian",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Leisen-Reimer
try {
europeanOption.setPricingEngine(
new BinomialLRVanillaEngine(stochasticProcess, timeSteps));
bermudanOption.setPricingEngine(
new BinomialLRVanillaEngine(stochasticProcess, timeSteps));
americanOption.setPricingEngine(
new BinomialLRVanillaEngine(stochasticProcess, timeSteps));
ReportResults("Binomial Leisen-Reimer",
europeanOption.NPV(),
bermudanOption.NPV(),
americanOption.NPV());
}
catch (Exception e) {
Console.WriteLine(e.ToString());
}
// Binomial Joshi
try {
europeanOption.setPricingEngine(
new BinomialJ4VanillaEngine(stochasticProcess, timeSteps));
bermudanOption.setPricingEngine(
new BinomialJ4VanillaEngine(stochasticProcess, timeSteps));
americanOption.setPricingEngine(
new BinomialJ4VanillaEngine(stochasticProcess, 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 {
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 MCPREuropeanEngine(stochasticProcess,
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 {
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 MCLDEuropeanEngine(stochasticProcess,
mcTimeSteps,
timeStepsPerYear,
brownianBridge,
antitheticVariate,
requiredSamples,
requiredTolerance,
maxSamples, seed));
ReportResults("MC (Sobol)", europeanOption.NPV(), 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();
}
//void testEngineConsistency(EngineType engine, int binomialSteps, int samples, Dictionary<string,double> tolerance,
// bool testGreeks = false) {
void testEngineConsistency(EngineType engine, int binomialSteps, int samples, Dictionary <string, double> tolerance,
bool testGreeks)
{
//QL_TEST_START_TIMING
Dictionary <string, double> calculated = new Dictionary <string, double>(), expected = new Dictionary <string, double>();
// test options
Option.Type[] types = { Option.Type.Call, Option.Type.Put };
double[] strikes = { 75.0, 100.0, 125.0 };
int[] lengths = { 1 };
// test data
double[] underlyings = { 100.0 };
double[] qRates = { 0.00, 0.05 };
double[] rRates = { 0.01, 0.05, 0.15 };
double[] vols = { 0.11, 0.50, 1.20 };
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(0.0);
SimpleQuote vol = new SimpleQuote(0.0);
BlackVolTermStructure volTS = Utilities.flatVol(today, vol, dc);
SimpleQuote qRate = new SimpleQuote(0.0);
YieldTermStructure qTS = Utilities.flatRate(today, qRate, dc);
SimpleQuote rRate = new SimpleQuote(0.0);
YieldTermStructure rTS = Utilities.flatRate(today, rRate, dc);
for (int i = 0; i < types.Length; i++)
{
for (int j = 0; j < strikes.Length; j++)
{
for (int k = 0; k < lengths.Length; k++)
{
Date exDate = today + lengths[k] * 360;
Exercise exercise = new EuropeanExercise(exDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(types[i], strikes[j]);
// reference option
VanillaOption refOption = makeOption(payoff, exercise, spot, qTS, rTS, volTS,
EngineType.Analytic, 0, 0);
// option to check
VanillaOption option = makeOption(payoff, exercise, spot, qTS, rTS, volTS,
engine, binomialSteps, samples);
for (int l = 0; l < underlyings.Length; l++)
{
for (int m = 0; m < qRates.Length; m++)
{
for (int n = 0; n < rRates.Length; n++)
{
for (int p = 0; p < vols.Length; p++)
{
double u = underlyings[l];
double q = qRates[m],
r = rRates[n];
double v = vols[p];
spot.setValue(u);
qRate.setValue(q);
rRate.setValue(r);
vol.setValue(v);
expected.Clear();
calculated.Clear();
// FLOATING_POINT_EXCEPTION
expected.Add("value", refOption.NPV());
calculated.Add("value", option.NPV());
if (testGreeks && option.NPV() > spot.value() * 1.0e-5)
{
expected.Add("delta", refOption.delta());
expected.Add("gamma", refOption.gamma());
expected.Add("theta", refOption.theta());
calculated.Add("delta", option.delta());
calculated.Add("gamma", option.gamma());
calculated.Add("theta", option.theta());
}
foreach (string greek in calculated.Keys)
{
double expct = expected[greek],
calcl = calculated[greek],
tol = tolerance[greek];
double error = Utilities.relativeError(expct, calcl, u);
if (error > tol)
{
REPORT_FAILURE(greek, payoff, exercise,
u, q, r, today, v,
expct, calcl, error, tol);
}
}
}
}
}
}
}
}
}
}
public void calculate(double[] p, GBMParaViewModel para)
{
this.xData_ = p;
this.yData_ = new double[p.Length];
double sellBuySign = 1.0;
if (this.sellBuy_ == "매도")
{
sellBuySign = -1.0;
}
else
{
}
// 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;
if (this.callPutEnum_ == Option.Type.Call)
{
this.imVol_ = para.Call_Interpolation_.value(this.strike_);
}
else if (this.callPutEnum_ == Option.Type.Put)
{
this.imVol_ = para.Put_Interpolation_.value(this.strike_);
}
double volatility = (this.imVol_) / 100;
Date maturity = new Date(this.maturiry_.AddDays(1));
if (this.callPutEnum_ == 0)
{
this.deltaCal_ = 1.0;
this.gammaCal_ = 0.0;
this.vegaCal_ = 0.0;
this.thetaCal_ = 0.0;
this.rhoCal_ = 0.0;
this.deltaPosition_ = sellBuySign * this.unit_ * 500000 * underlying;
this.deltaRisk_ = this.deltaPosition_ * 0.09;
this.gammaRisk_ = 0.0;
this.vegaRisk_ = 0.0;
this.totalRisk_ = this.deltaRisk_ + this.gammaRisk_ + this.vegaRisk_;
this.deepOTM_ = 0.0;
//this.remainDays_ = maturity - settlementDate;
this.remainDays_ = (this.maturiry_ - para.ReferenceDate_).Days + 1;
return;
}
DayCounter dayCounter = new Actual365Fixed();
Exercise europeanExercise = new EuropeanExercise(maturity);
SimpleQuote quote = new SimpleQuote(underlying);
Handle <Quote> underlyingH = new Handle <Quote>(quote);
// 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_ = sellBuySign * Math.Round(europeanOption.delta(), 6);
this.gammaCal_ = sellBuySign * Math.Round(europeanOption.gamma(), 6);
this.vegaCal_ = sellBuySign * Math.Round(europeanOption.vega() / 100, 6);
this.thetaCal_ = sellBuySign * Math.Round(europeanOption.theta() / 365, 6);
this.rhoCal_ = sellBuySign * Math.Round(europeanOption.rho() / 100, 6);
this.deltaPosition_ = Math.Round(this.deltaCal_ * this.unit_ * 500000 * underlying, 0);
this.deltaRisk_ = Math.Round(this.deltaPosition_ * 0.09, 0);
this.gammaRisk_ = Math.Round(0.5 * this.gammaCal_ * (underlying * underlying * 0.08 * 0.08) * this.unit_ * 500000, 0);
this.vegaRisk_ = Math.Round(this.vegaCal_ * this.imVol_ * 0.25 * this.unit_ * 500000, 0);
this.totalRisk_ = this.deltaRisk_ + this.gammaRisk_ + this.vegaRisk_;
this.deepOTM_ = 0.0;
//this.remainDays_ = maturity - settlementDate;
this.remainDays_ = (this.maturiry_ - para.ReferenceDate_).Days + 1;
for (int i = 0; i < this.xData_.Length; i++)
{
quote.setValue(this.xData_[i]);
this.yData_[i] = 500000.0 * (double)this.unit_ * europeanOption.NPV();
}
}
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);
}
