public HybridHestonHullWhiteProcess(HestonProcess hestonProcess,
HullWhiteForwardProcess hullWhiteProcess,
double corrEquityShortRate,
Discretization discretization = Discretization.BSMHullWhite)
{
hestonProcess_ = hestonProcess;
hullWhiteProcess_ = hullWhiteProcess;
hullWhiteModel_ = new HullWhite(hestonProcess.riskFreeRate(),
hullWhiteProcess.a(),
hullWhiteProcess.sigma());
corrEquityShortRate_ = corrEquityShortRate;
disc_ = discretization;
maxRho_ = Math.Sqrt(1 - hestonProcess.rho() * hestonProcess.rho())
- Math.Sqrt(Const.QL_EPSILON) /* reserve for rounding errors */;
T_ = hullWhiteProcess.getForwardMeasureTime();
endDiscount_ = hestonProcess.riskFreeRate().link.discount(T_);
Utils.QL_REQUIRE(corrEquityShortRate * corrEquityShortRate
+ hestonProcess.rho() * hestonProcess.rho() <= 1.0, () =>
"correlation matrix is not positive definite");
Utils.QL_REQUIRE(hullWhiteProcess.sigma() > 0.0, () =>
"positive vol of Hull White process is required");
}
public AnalyticH1HWEngine(HestonModel model, HullWhite hullWhiteModel, double rhoSr, int integrationOrder = 144)
: base(model, hullWhiteModel, integrationOrder)
{
rhoSr_ = rhoSr;
Utils.QL_REQUIRE(rhoSr_ >= 0.0, () => "Fourier integration is not stable if " +
"the equity interest rate correlation is negative");
}
public AnalyticHestonHullWhiteEngine(HestonModel hestonModel,
HullWhite hullWhiteModel,
double relTolerance, int maxEvaluations)
: base(hestonModel, relTolerance, maxEvaluations)
{
hullWhiteModel_ = hullWhiteModel;
update();
hullWhiteModel_.registerWith(update);
}
// see AnalticHestonEninge for usage of different constructors
public AnalyticHestonHullWhiteEngine(HestonModel hestonModel,
HullWhite hullWhiteModel,
int integrationOrder = 144)
: base(hestonModel, integrationOrder)
{
hullWhiteModel_ = hullWhiteModel;
update();
hullWhiteModel_.registerWith(update);
}
public FdmHullWhiteOp(FdmMesher mesher,
HullWhite model,
int direction)
{
x_ = mesher.locations(direction);
dzMap_ = new TripleBandLinearOp(new FirstDerivativeOp(direction, mesher).mult(-1.0 * x_ * model.a()).add(
new SecondDerivativeOp(direction, mesher).mult(0.5 * model.sigma() * model.sigma()
* new Vector(mesher.layout().size(), 1.0))));
mapT_ = new TripleBandLinearOp(direction, mesher);
direction_ = direction;
model_ = model;
}
public Fj_Helper(Handle <HestonModel> hestonModel, HullWhite hullWhiteModel, double rhoSr, double term,
double strike, int j)
{
j_ = j;
lambda_ = hullWhiteModel.a();
eta_ = hullWhiteModel.sigma();
v0_ = hestonModel.link.v0();
kappa_ = hestonModel.link.kappa();
theta_ = hestonModel.link.theta();
gamma_ = hestonModel.link.sigma();
d_ = 4.0 * kappa_ * theta_ / (gamma_ * gamma_);
rhoSr_ = rhoSr;
term_ = term;
}
protected override IPricingEngine controlPricingEngine()
{
HybridHestonHullWhiteProcess process = process_ as HybridHestonHullWhiteProcess;
Utils.QL_REQUIRE(process != null, () => "invalid process");
HestonProcess hestonProcess = process.hestonProcess();
HullWhiteForwardProcess hullWhiteProcess = process.hullWhiteProcess();
HestonModel hestonModel = new HestonModel(hestonProcess);
HullWhite hwModel = new HullWhite(hestonProcess.riskFreeRate(),
hullWhiteProcess.a(),
hullWhiteProcess.sigma());
return(new AnalyticHestonHullWhiteEngine(hestonModel, hwModel, 144));
}
public AnalyticH1HWEngine(HestonModel model, HullWhite hullWhiteModel, double rhoSr, double relTolerance,
int maxEvaluations)
: base(model, hullWhiteModel, relTolerance, maxEvaluations)
{
rhoSr_ = rhoSr;
}
public void testCachedValues()
{
//("Testing Bermudan swaption against cached values...");
CommonVars vars = new CommonVars();
vars.today = new Date(15, Month.February, 2002);
Settings.setEvaluationDate(vars.today);
vars.settlement = new Date(19, Month.February, 2002);
// flat yield term structure impling 1x5 swap at 5%
vars.termStructure.linkTo(Utilities.flatRate(vars.settlement,
0.04875825,
new Actual365Fixed()));
double atmRate = vars.makeSwap(0.0).fairRate();
VanillaSwap itmSwap = vars.makeSwap(0.8*atmRate);
VanillaSwap atmSwap = vars.makeSwap(atmRate);
VanillaSwap otmSwap = vars.makeSwap(1.2*atmRate);
double a = 0.048696, sigma = 0.0058904;
ShortRateModel model=new HullWhite(vars.termStructure,a, sigma);
List<Date> exerciseDates= new List<Date>();
List<CashFlow> leg = atmSwap.fixedLeg();
for (int i=0; i<leg.Count; i++) {
Coupon coupon = (Coupon)(leg[i]);
exerciseDates.Add(coupon.accrualStartDate());
}
Exercise exercise = new BermudanExercise(exerciseDates);
IPricingEngine engine = new TreeSwaptionEngine(model, 50);
#if QL_USE_INDEXED_COUPON
Real itmValue = 42.2413, atmValue = 12.8789, otmValue = 2.4759;
#else
double itmValue = 42.2470, atmValue = 12.8826, otmValue = 2.4769;
#endif
double tolerance = 1.0e-4;
Swaption swaption = new Swaption(itmSwap, exercise);
swaption.setPricingEngine(engine);
if (Math.Abs(swaption.NPV()-itmValue) > tolerance)
Assert.Fail("failed to reproduce cached in-the-money swaption value:\n"
+ "calculated: " + swaption.NPV() + "\n"
+ "expected: " + itmValue);
swaption = new Swaption(atmSwap, exercise);
swaption.setPricingEngine(engine);
if (Math.Abs(swaption.NPV()-atmValue) > tolerance)
Assert.Fail("failed to reproduce cached at-the-money swaption value:\n"
+ "calculated: " + swaption.NPV() + "\n"
+ "expected: " + atmValue);
swaption = new Swaption(otmSwap, exercise);
swaption.setPricingEngine(engine);
if (Math.Abs(swaption.NPV()-otmValue) > tolerance)
Assert.Fail("failed to reproduce cached out-of-the-money "
+ "swaption value:\n"
+ "calculated: " + swaption.NPV() + "\n"
+ "expected: " + otmValue);
for (int j=0; j<exerciseDates.Count; j++)
exerciseDates[j] = vars.calendar.adjust(exerciseDates[j]-10);
exercise = new BermudanExercise(exerciseDates);
#if QL_USE_INDEXED_COUPON
itmValue = 42.1917; atmValue = 12.7788; otmValue = 2.4388;
#else
itmValue = 42.1974; atmValue = 12.7825; otmValue = 2.4399;
#endif
swaption = new Swaption(itmSwap, exercise);
swaption.setPricingEngine(engine);
if (Math.Abs(swaption.NPV()-itmValue) > tolerance)
Assert.Fail("failed to reproduce cached in-the-money swaption value:\n"
+ "calculated: " + swaption.NPV() + "\n"
+ "expected: " + itmValue);
swaption = new Swaption(atmSwap, exercise);
swaption.setPricingEngine(engine);
if (Math.Abs(swaption.NPV()-atmValue) > tolerance)
Assert.Fail("failed to reproduce cached at-the-money swaption value:\n"
+ "calculated: " + swaption.NPV() + "\n"
+ "expected: " + atmValue);
swaption = new Swaption(otmSwap, exercise);
swaption.setPricingEngine(engine);
if (Math.Abs(swaption.NPV()-otmValue) > tolerance)
Assert.Fail("failed to reproduce cached out-of-the-money "
+ "swaption value:\n"
+ "calculated: " + swaption.NPV() + "\n"
+ "expected: " + otmValue);
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
Date todaysDate = new Date(15, 2, 2002);
Calendar calendar = new TARGET();
Date settlementDate = new Date(19, 2, 2002);
Settings.setEvaluationDate(todaysDate);
// flat yield term structure impling 1x5 swap at 5%
Quote flatRate = new SimpleQuote(0.04875825);
Handle<YieldTermStructure> rhTermStructure = new Handle<YieldTermStructure>(
new FlatForward(settlementDate, new Handle<Quote>(flatRate),
new Actual365Fixed()));
// Define the ATM/OTM/ITM swaps
Frequency fixedLegFrequency = Frequency.Annual;
BusinessDayConvention fixedLegConvention = BusinessDayConvention.Unadjusted;
BusinessDayConvention floatingLegConvention = BusinessDayConvention.ModifiedFollowing;
DayCounter fixedLegDayCounter = new Thirty360(Thirty360.Thirty360Convention.European);
Frequency floatingLegFrequency = Frequency.Semiannual;
VanillaSwap.Type type = VanillaSwap.Type.Payer;
double dummyFixedRate = 0.03;
IborIndex indexSixMonths = new Euribor6M(rhTermStructure);
Date startDate = calendar.advance(settlementDate, 1, TimeUnit.Years,
floatingLegConvention);
Date maturity = calendar.advance(startDate, 5, TimeUnit.Years,
floatingLegConvention);
Schedule fixedSchedule = new Schedule(startDate, maturity, new Period(fixedLegFrequency),
calendar, fixedLegConvention, fixedLegConvention,
DateGeneration.Rule.Forward, false);
Schedule floatSchedule = new Schedule(startDate, maturity, new Period(floatingLegFrequency),
calendar, floatingLegConvention, floatingLegConvention,
DateGeneration.Rule.Forward, false);
VanillaSwap swap = new VanillaSwap(
type, 1000.0,
fixedSchedule, dummyFixedRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
swap.setPricingEngine(new DiscountingSwapEngine(rhTermStructure));
double fixedAtmRate = swap.fairRate();
double fixedOtmRate = fixedAtmRate * 1.2;
double fixedItmRate = fixedAtmRate * 0.8;
VanillaSwap atmSwap = new VanillaSwap(
type, 1000.0,
fixedSchedule, fixedAtmRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
VanillaSwap otmSwap = new VanillaSwap(
type, 1000.0,
fixedSchedule, fixedOtmRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
VanillaSwap itmSwap = new VanillaSwap(
type, 1000.0,
fixedSchedule, fixedItmRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
// defining the swaptions to be used in model calibration
List<Period> swaptionMaturities = new List<Period>(5);
swaptionMaturities.Add(new Period(1, TimeUnit.Years));
swaptionMaturities.Add(new Period(2, TimeUnit.Years));
swaptionMaturities.Add(new Period(3, TimeUnit.Years));
swaptionMaturities.Add(new Period(4, TimeUnit.Years));
swaptionMaturities.Add(new Period(5, TimeUnit.Years));
List<CalibrationHelper> swaptions = new List<CalibrationHelper>();
// List of times that have to be included in the timegrid
List<double> times = new List<double>();
for (int i = 0; i < NumRows; i++)
{
int j = NumCols - i - 1; // 1x5, 2x4, 3x3, 4x2, 5x1
int k = i * NumCols + j;
Quote vol = new SimpleQuote(SwaptionVols[k]);
swaptions.Add(new SwaptionHelper(swaptionMaturities[i],
new Period(SwapLenghts[j], TimeUnit.Years),
new Handle<Quote>(vol),
indexSixMonths,
indexSixMonths.tenor(),
indexSixMonths.dayCounter(),
indexSixMonths.dayCounter(),
rhTermStructure, false));
swaptions.Last().addTimesTo(times);
}
// Building time-grid
TimeGrid grid = new TimeGrid(times, 30);
// defining the models
G2 modelG2 = new G2(rhTermStructure);
HullWhite modelHw = new HullWhite(rhTermStructure);
HullWhite modelHw2 = new HullWhite(rhTermStructure);
BlackKarasinski modelBk = new BlackKarasinski(rhTermStructure);
// model calibrations
Console.WriteLine("G2 (analytic formulae) calibration");
for (int i = 0; i < swaptions.Count; i++)
swaptions[i].setPricingEngine(new G2SwaptionEngine(modelG2, 6.0, 16));
CalibrateModel(modelG2, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.0000000}\n" +
"b = {2:0.000000}, " +
"eta = {3:0.0000000}\n" +
"rho = {4:0.00000}\n",
modelG2.parameters()[0],
modelG2.parameters()[1],
modelG2.parameters()[2],
modelG2.parameters()[3],
modelG2.parameters()[4]);
Console.WriteLine("Hull-White (analytic formulae) calibration");
for (int i = 0; i < swaptions.Count; i++)
swaptions[i].setPricingEngine(new JamshidianSwaptionEngine(modelHw));
CalibrateModel(modelHw, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.0000000}\n",
modelHw.parameters()[0],
modelHw.parameters()[1]);
Console.WriteLine("Hull-White (numerical) calibration");
for (int i = 0; i < swaptions.Count(); i++)
swaptions[i].setPricingEngine(new TreeSwaptionEngine(modelHw2, grid));
CalibrateModel(modelHw2, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.0000000}\n",
modelHw2.parameters()[0],
modelHw2.parameters()[1]);
Console.WriteLine("Black-Karasinski (numerical) calibration");
for (int i = 0; i < swaptions.Count; i++)
swaptions[i].setPricingEngine(new TreeSwaptionEngine(modelBk, grid));
CalibrateModel(modelBk, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.00000}\n",
modelBk.parameters()[0],
modelBk.parameters()[1]);
// ATM Bermudan swaption pricing
Console.WriteLine("Payer bermudan swaption "
+ "struck at {0:0.00000 %} (ATM)",
fixedAtmRate);
List<Date> bermudanDates = new List<Date>();
List<CashFlow> leg = swap.fixedLeg();
for (int i = 0; i < leg.Count; i++)
{
Coupon coupon = (Coupon)leg[i];
bermudanDates.Add(coupon.accrualStartDate());
}
Exercise bermudanExercise = new BermudanExercise(bermudanDates);
Swaption bermudanSwaption = new Swaption(atmSwap, bermudanExercise);
// Do the pricing for each model
// G2 price the European swaption here, it should switch to bermudan
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelG2, 50));
Console.WriteLine("G2: {0:0.00}", bermudanSwaption.NPV());
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw, 50));
Console.WriteLine("HW: {0:0.000}", bermudanSwaption.NPV());
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw2, 50));
Console.WriteLine("HW (num): {0:0.000}", bermudanSwaption.NPV());
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelBk, 50));
Console.WriteLine("BK: {0:0.000}", bermudanSwaption.NPV());
// OTM Bermudan swaption pricing
Console.WriteLine("Payer bermudan swaption "
+ "struck at {0:0.00000 %} (OTM)",
fixedOtmRate);
Swaption otmBermudanSwaption = new Swaption(otmSwap, bermudanExercise);
// Do the pricing for each model
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelG2, 50));
Console.WriteLine("G2: {0:0.0000}", otmBermudanSwaption.NPV());
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw, 50));
Console.WriteLine("HW: {0:0.0000}", otmBermudanSwaption.NPV());
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw2, 50));
Console.WriteLine("HW (num): {0:0.000}", otmBermudanSwaption.NPV());
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelBk, 50));
Console.WriteLine("BK: {0:0.0000}", otmBermudanSwaption.NPV());
// ITM Bermudan swaption pricing
Console.WriteLine("Payer bermudan swaption "
+ "struck at {0:0.00000 %} (ITM)",
fixedItmRate);
Swaption itmBermudanSwaption = new Swaption(itmSwap, bermudanExercise);
// Do the pricing for each model
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelG2, 50));
Console.WriteLine("G2: {0:0.000}", itmBermudanSwaption.NPV());
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw, 50));
Console.WriteLine("HW: {0:0.000}", itmBermudanSwaption.NPV());
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw2, 50));
Console.WriteLine("HW (num): {0:0.000}", itmBermudanSwaption.NPV());
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelBk, 50));
Console.WriteLine("BK: {0:0.000}", itmBermudanSwaption.NPV());
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
public void testCachedHullWhite()
{
//("Testing Hull-White calibration against cached values...");
Date today=new Date(15, Month.February, 2002);
Date settlement=new Date(19, Month.February, 2002);
Settings.setEvaluationDate(today);
Handle<YieldTermStructure> termStructure=
new Handle<YieldTermStructure>(Utilities.flatRate(settlement, 0.04875825, new Actual365Fixed()));
//termStructure.link
HullWhite model=new HullWhite(termStructure);
CalibrationData[] data = { new CalibrationData( 1, 5, 0.1148 ),
new CalibrationData( 2, 4, 0.1108 ),
new CalibrationData( 3, 3, 0.1070 ),
new CalibrationData( 4, 2, 0.1021 ),
new CalibrationData( 5, 1, 0.1000 )};
IborIndex index = new Euribor6M(termStructure);
IPricingEngine engine = new JamshidianSwaptionEngine(model);
List<CalibrationHelper> swaptions = new List<CalibrationHelper>();
for (int i=0; i<data.Length; i++) {
Quote vol = new SimpleQuote(data[i].volatility);
CalibrationHelper helper =
new SwaptionHelper(new Period(data[i].start,TimeUnit.Years),
new Period(data[i].length, TimeUnit.Years),
new Handle<Quote>(vol),
index,
new Period(1, TimeUnit.Years),
new Thirty360(),
new Actual360(),
termStructure);
helper.setPricingEngine(engine);
swaptions.Add(helper);
}
// Set up the optimization problem
// Real simplexLambda = 0.1;
// Simplex optimizationMethod(simplexLambda);
LevenbergMarquardt optimizationMethod = new LevenbergMarquardt(1.0e-8,1.0e-8,1.0e-8);
EndCriteria endCriteria = new EndCriteria(10000, 100, 1e-6, 1e-8, 1e-8);
//Optimize
model.calibrate(swaptions, optimizationMethod, endCriteria, new Constraint(),new List<double>());
EndCriteria.Type ecType = model.endCriteria();
// Check and print out results
#if QL_USE_INDEXED_COUPON
double cachedA = 0.0488199, cachedSigma = 0.00593579;
#else
double cachedA = 0.0488565, cachedSigma = 0.00593662;
#endif
double tolerance = 1.120e-5;
//double tolerance = 1.0e-6;
Vector xMinCalculated = model.parameters();
double yMinCalculated = model.value(xMinCalculated, swaptions);
Vector xMinExpected = new Vector(2);
xMinExpected[0]= cachedA;
xMinExpected[1]= cachedSigma;
double yMinExpected = model.value(xMinExpected, swaptions);
if (Math.Abs(xMinCalculated[0]-cachedA) > tolerance
|| Math.Abs(xMinCalculated[1]-cachedSigma) > tolerance) {
Assert.Fail ("Failed to reproduce cached calibration results:\n"
+ "calculated: a = " + xMinCalculated[0] + ", "
+ "sigma = " + xMinCalculated[1] + ", "
+ "f(a) = " + yMinCalculated + ",\n"
+ "expected: a = " + xMinExpected[0] + ", "
+ "sigma = " + xMinExpected[1] + ", "
+ "f(a) = " + yMinExpected + ",\n"
+ "difference: a = " + (xMinCalculated[0]-xMinExpected[0]) + ", "
+ "sigma = " + (xMinCalculated[1]-xMinExpected[1]) + ", "
+ "f(a) = " + (yMinCalculated - yMinExpected) + ",\n"
+ "end criteria = " + ecType );
}
}
public void testSwaps()
{
//BOOST_MESSAGE("Testing Hull-White swap pricing against known values...");
Date today; //=Settings::instance().evaluationDate();;
Calendar calendar = new TARGET();
today = calendar.adjust(Date.Today);
Settings.setEvaluationDate(today);
Date settlement = calendar.advance(today, 2, TimeUnit.Days);
Date[] dates = {
settlement,
calendar.advance(settlement,1,TimeUnit.Weeks),
calendar.advance(settlement,1,TimeUnit.Months),
calendar.advance(settlement,3,TimeUnit.Months),
calendar.advance(settlement,6,TimeUnit.Months),
calendar.advance(settlement,9,TimeUnit.Months),
calendar.advance(settlement,1,TimeUnit.Years),
calendar.advance(settlement,2,TimeUnit.Years),
calendar.advance(settlement,3,TimeUnit.Years),
calendar.advance(settlement,5,TimeUnit.Years),
calendar.advance(settlement,10,TimeUnit.Years),
calendar.advance(settlement,15,TimeUnit.Years)
};
double[] discounts = {
1.0,
0.999258,
0.996704,
0.990809,
0.981798,
0.972570,
0.963430,
0.929532,
0.889267,
0.803693,
0.596903,
0.433022
};
//for (int i = 0; i < dates.Length; i++)
// dates[i] + dates.Length;
LogLinear Interpolator = new LogLinear();
Handle<YieldTermStructure> termStructure =
new Handle<YieldTermStructure>(
new InterpolatedDiscountCurve<LogLinear>(
dates.ToList<Date>(),
discounts.ToList<double>(),
new Actual365Fixed(),new Calendar(), null, null , Interpolator)
);
HullWhite model = new HullWhite(termStructure);
int[] start = { -3, 0, 3 };
int[] length = { 2, 5, 10 };
double[] rates = { 0.02, 0.04, 0.06 };
IborIndex euribor = new Euribor6M(termStructure);
IPricingEngine engine = new TreeVanillaSwapEngine(model, 120, termStructure);
#if QL_USE_INDEXED_COUPON
double tolerance = 4.0e-3;
#else
double tolerance = 1.0e-8;
#endif
for (int i=0; i<start.Length; i++) {
Date startDate = calendar.advance(settlement,start[i],TimeUnit.Months);
if (startDate < today) {
Date fixingDate = calendar.advance(startDate,-2,TimeUnit.Days);
//TimeSeries<double> pastFixings;
ObservableValue<TimeSeries<double>> pastFixings = new ObservableValue<TimeSeries<double>>();
pastFixings.value()[fixingDate] = 0.03;
IndexManager.instance().setHistory(euribor.name(),
pastFixings);
}
for (int j=0; j<length.Length; j++) {
Date maturity = calendar.advance(startDate, length[i], TimeUnit.Years);
Schedule fixedSchedule = new Schedule(startDate, maturity, new Period(Frequency.Annual),
calendar, BusinessDayConvention.Unadjusted, BusinessDayConvention.Unadjusted,
DateGeneration.Rule.Forward, false);
Schedule floatSchedule = new Schedule(startDate, maturity, new Period(Frequency.Semiannual),
calendar, BusinessDayConvention.Following, BusinessDayConvention.Following,
DateGeneration.Rule.Forward, false);
for (int k=0; k<rates.Length; k++) {
VanillaSwap swap = new VanillaSwap(VanillaSwap.Type.Payer, 1000000.0,
fixedSchedule, rates[k], new Thirty360(),
floatSchedule, euribor, 0.0, new Actual360());
swap.setPricingEngine(new DiscountingSwapEngine(termStructure));
double expected = swap.NPV();
swap.setPricingEngine(engine);
double calculated = swap.NPV();
double error = Math.Abs((expected-calculated)/expected);
if (error > tolerance) {
Assert.Fail("Failed to reproduce swap NPV:"
//+ QL_FIXED << std::setprecision(9)
+ "\n calculated: " + calculated
+ "\n expected: " + expected
//+ QL_SCIENTIFIC
+ "\n rel. error: " + error);
}
}
}
}
}
static void Main(string[] args)
{
// boost::timer timer;
Date today = new Date(16,Month.October,2007);
Settings.setEvaluationDate(today);
Console.WriteLine();
Console.WriteLine("Pricing a callable fixed rate bond using");
Console.WriteLine("Hull White model w/ reversion parameter = 0.03");
Console.WriteLine("BAC4.65 09/15/12 ISIN: US06060WBJ36");
Console.WriteLine("roughly five year tenor, ");
Console.WriteLine("quarterly coupon and call dates");
Console.WriteLine("reference date is : " + today );
/* Bloomberg OAS1: "N" model (Hull White)
varying volatility parameter
The curve entered into Bloomberg OAS1 is a flat curve,
at constant yield = 5.5%, semiannual compounding.
Assume here OAS1 curve uses an ACT/ACT day counter,
as documented in PFC1 as a "default" in the latter case.
*/
// set up a flat curve corresponding to Bloomberg flat curve
double bbCurveRate = 0.055;
DayCounter bbDayCounter = new ActualActual(ActualActual.Convention.Bond);
InterestRate bbIR = new InterestRate(bbCurveRate,bbDayCounter,Compounding.Compounded ,Frequency.Semiannual);
Handle<YieldTermStructure> termStructure = new Handle<YieldTermStructure>(flatRate( today,
bbIR.rate(),
bbIR.dayCounter(),
bbIR.compounding(),
bbIR.frequency()));
// set up the call schedule
CallabilitySchedule callSchedule = new CallabilitySchedule();
double callPrice = 100.0;
int numberOfCallDates = 24;
Date callDate = new Date(15,Month.September,2006);
for (int i=0; i< numberOfCallDates; i++)
{
Calendar nullCalendar = new NullCalendar();
Callability.Price myPrice = new Callability.Price(callPrice, Callability.Price.Type.Clean);
callSchedule.Add( new Callability(myPrice,Callability.Type.Call, callDate ));
callDate = nullCalendar.advance(callDate, 3, TimeUnit.Months);
}
// set up the callable bond
Date dated = new Date(16,Month.September,2004);
Date issue = dated;
Date maturity = new Date(15,Month.September,2012);
int settlementDays = 3; // Bloomberg OAS1 settle is Oct 19, 2007
Calendar bondCalendar = new UnitedStates(UnitedStates.Market.GovernmentBond);
double coupon = .0465;
Frequency frequency = Frequency.Quarterly;
double redemption = 100.0;
double faceAmount = 100.0;
/* The 30/360 day counter Bloomberg uses for this bond cannot
reproduce the US Bond/ISMA (constant) cashflows used in PFC1.
Therefore use ActAct(Bond)
*/
DayCounter bondDayCounter = new ActualActual(ActualActual.Convention.Bond);
// PFC1 shows no indication dates are being adjusted
// for weekends/holidays for vanilla bonds
BusinessDayConvention accrualConvention = BusinessDayConvention.Unadjusted;
BusinessDayConvention paymentConvention = BusinessDayConvention.Unadjusted;
Schedule sch = new Schedule( dated, maturity, new Period(frequency), bondCalendar,
accrualConvention, accrualConvention,
DateGeneration.Rule.Backward, false);
int maxIterations = 1000;
double accuracy = 1e-8;
int gridIntervals = 40;
double reversionParameter = .03;
// output price/yield results for varying volatility parameter
double sigma = Const.QL_Epsilon; // core dumps if zero on Cygwin
ShortRateModel hw0 = new HullWhite(termStructure,reversionParameter,sigma);
IPricingEngine engine0 = new TreeCallableFixedRateBondEngine(hw0, gridIntervals, termStructure);
CallableFixedRateBond callableBond = new CallableFixedRateBond( settlementDays, faceAmount, sch,
new InitializedList<double>(1, coupon),
bondDayCounter, paymentConvention,
redemption, issue, callSchedule);
callableBond.setPricingEngine(engine0);
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine( "{0:0.00} / {1:0.00} ", callableBond.cleanPrice() ,
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("96.50 / 5.47");
//
sigma = .01;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw1 = new HullWhite(termStructure,reversionParameter,sigma);
IPricingEngine engine1 = new TreeCallableFixedRateBondEngine(hw1,gridIntervals,termStructure);
callableBond.setPricingEngine(engine1);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine( "{0:0.00} / {1:0.00} ", callableBond.cleanPrice() ,
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("95.68 / 5.66");
//
sigma = .03;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw2 = new HullWhite(termStructure, reversionParameter, sigma);
IPricingEngine engine2 = new TreeCallableFixedRateBondEngine(hw2, gridIntervals, termStructure);
callableBond.setPricingEngine(engine2);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine("{0:0.00} / {1:0.00} ", callableBond.cleanPrice(),
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("92.34 / 6.49");
//
sigma = .06;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw3 = new HullWhite(termStructure, reversionParameter, sigma);
IPricingEngine engine3 = new TreeCallableFixedRateBondEngine(hw3, gridIntervals, termStructure);
callableBond.setPricingEngine(engine3);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine("{0:0.00} / {1:0.00} ", callableBond.cleanPrice(),
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("87.16 / 7.83");
//
sigma = .12;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw4 = new HullWhite(termStructure, reversionParameter, sigma);
IPricingEngine engine4 = new TreeCallableFixedRateBondEngine(hw4, gridIntervals, termStructure);
callableBond.setPricingEngine(engine4);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine("{0:0.00} / {1:0.00} ", callableBond.cleanPrice(),
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("77.31 / 10.65");
}
