public FdHestonVanillaEngine(HestonModel model, uint tGrid) : this(NQuantLibcPINVOKE.new_FdHestonVanillaEngine__SWIG_5(HestonModel.getCPtr(model), tGrid), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public FdHestonVanillaEngine(HestonModel model, uint tGrid, uint xGrid, uint vGrid, uint dampingSteps, FdmSchemeDesc schemeDesc, LocalVolTermStructure leverageFct) : this(NQuantLibcPINVOKE.new_FdHestonVanillaEngine__SWIG_0(HestonModel.getCPtr(model), tGrid, xGrid, vGrid, dampingSteps, FdmSchemeDesc.getCPtr(schemeDesc), LocalVolTermStructure.getCPtr(leverageFct)), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public AnalyticHestonEngine(HestonModel model, double relTolerance, uint maxEvaluations) : this(NQuantLibcPINVOKE.new_AnalyticHestonEngine__SWIG_2(HestonModel.getCPtr(model), relTolerance, maxEvaluations), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public COSHestonEngine(HestonModel model, double L) : this(NQuantLibcPINVOKE.new_COSHestonEngine__SWIG_1(HestonModel.getCPtr(model), L), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public FdHestonDoubleBarrierEngine(HestonModel model) : this(NQuantLibcPINVOKE.new_FdHestonDoubleBarrierEngine__SWIG_6(HestonModel.getCPtr(model)), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public HestonModelHandle(HestonModel arg0) : this(NQuantLibcPINVOKE.new_HestonModelHandle__SWIG_0(HestonModel.getCPtr(arg0)), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public FdHestonDoubleBarrierEngine(HestonModel model, uint tGrid, uint xGrid, uint vGrid, uint dampingSteps, FdmSchemeDesc schemeDesc) : this(NQuantLibcPINVOKE.new_FdHestonDoubleBarrierEngine__SWIG_1(HestonModel.getCPtr(model), tGrid, xGrid, vGrid, dampingSteps, FdmSchemeDesc.getCPtr(schemeDesc)), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public FdHestonDoubleBarrierEngine(HestonModel model, uint tGrid, uint xGrid, uint vGrid) : this(NQuantLibcPINVOKE.new_FdHestonDoubleBarrierEngine__SWIG_3(HestonModel.getCPtr(model), tGrid, xGrid, vGrid), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public AnalyticHestonEngine(HestonModel model) : this(NQuantLibcPINVOKE.new_AnalyticHestonEngine__SWIG_1(HestonModel.getCPtr(model)), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public AnalyticHestonEngine(HestonModel model, AnalyticHestonEngine.ComplexLogFormula cpxLog, AnalyticHestonEngine.AnalyticHestonEngine_Integration itg) : this(NQuantLibcPINVOKE.new_AnalyticHestonEngine__SWIG_4(HestonModel.getCPtr(model), (int)cpxLog, AnalyticHestonEngine.AnalyticHestonEngine_Integration.getCPtr(itg)), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public HestonSLVFDMModel(LocalVolTermStructure localVol, HestonModel model, Date endDate, HestonSLVFokkerPlanckFdmParams params_) : this(NQuantLibcPINVOKE.new_HestonSLVFDMModel__SWIG_2(LocalVolTermStructure.getCPtr(localVol), HestonModel.getCPtr(model), Date.getCPtr(endDate), HestonSLVFokkerPlanckFdmParams.getCPtr(params_)), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public HestonSLVMCModel(LocalVolTermStructure localVol, HestonModel model, BrownianGeneratorFactory brownianGeneratorFactory, Date endDate) : this(NQuantLibcPINVOKE.new_HestonSLVMCModel__SWIG_4(LocalVolTermStructure.getCPtr(localVol), HestonModel.getCPtr(model), BrownianGeneratorFactory.getCPtr(brownianGeneratorFactory), Date.getCPtr(endDate)), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public HestonSLVMCModel(LocalVolTermStructure localVol, HestonModel model, BrownianGeneratorFactory brownianGeneratorFactory, Date endDate, uint timeStepsPerYear, uint nBins, uint calibrationPaths) : this(NQuantLibcPINVOKE.new_HestonSLVMCModel__SWIG_1(LocalVolTermStructure.getCPtr(localVol), HestonModel.getCPtr(model), BrownianGeneratorFactory.getCPtr(brownianGeneratorFactory), Date.getCPtr(endDate), timeStepsPerYear, nBins, calibrationPaths), true)
{
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
}
public HestonModel __deref__()
{
global::System.IntPtr cPtr = NQuantLibcPINVOKE.HestonModelHandle___deref__(swigCPtr);
HestonModel ret = (cPtr == global::System.IntPtr.Zero) ? null : new HestonModel(cPtr, true);
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
return(ret);
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(HestonModel obj)
{
return((obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr);
}
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]);
}
}
}
}
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 testCompareBsmHWandHestonHW()
{
// Comparing European option pricing for a BSM process with one-factor Hull-White model
DayCounter dc = new Actual365Fixed();
Date today = Date.Today;
Settings.Instance.setEvaluationDate(today);
Handle <Quote> spot = new Handle <Quote>(new SimpleQuote(100.0));
List <Date> dates = new List <Date>();
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(0.01 + 0.0002 * Math.Exp(Math.Sin(i / 4.0)));
divRates.Add(0.02 + 0.0001 * Math.Exp(Math.Sin(i / 5.0)));
}
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));
SimpleQuote vol = new SimpleQuote(0.25);
Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(today, vol, dc));
BlackScholesMertonProcess bsmProcess = new BlackScholesMertonProcess(spot, qTS, rTS, volTS);
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, spot,
vol.value() * vol.value(), 1.0, vol.value() * vol.value(), 1e-4, 0.0);
HestonModel hestonModel = new HestonModel(hestonProcess);
HullWhite hullWhiteModel = new HullWhite(new Handle <YieldTermStructure>(rTS), 0.01, 0.01);
IPricingEngine bsmhwEngine = new AnalyticBSMHullWhiteEngine(0.0, bsmProcess, hullWhiteModel);
IPricingEngine hestonHwEngine = new AnalyticHestonHullWhiteEngine(hestonModel, hullWhiteModel, 128);
double tol = 1e-5;
double[] strike = { 0.25, 0.5, 0.75, 0.8, 0.9, 1.0, 1.1, 1.2, 1.5, 2.0, 4.0 };
int[] maturity = { 1, 2, 3, 5, 10, 15, 20, 25, 30 };
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)
{
for (int l = 0; l < maturity.Length; ++l)
{
Date maturityDate = today + new Period(maturity[l], TimeUnit.Years);
Exercise exercise = new EuropeanExercise(maturityDate);
double fwd = strike[j] * spot.link.value()
* qTS.link.discount(maturityDate) / rTS.link.discount(maturityDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(types[i], fwd);
EuropeanOption option = new EuropeanOption(payoff, exercise);
option.setPricingEngine(bsmhwEngine);
double calculated = option.NPV();
option.setPricingEngine(hestonHwEngine);
double expected = option.NPV();
if (Math.Abs(calculated - expected) > calculated * tol &&
Math.Abs(calculated - expected) > tol)
{
QAssert.Fail("Failed to reproduce npvs"
+ "\n calculated: " + calculated
+ "\n expected : " + expected
+ "\n strike : " + strike[j]
+ "\n maturity : " + maturity[l]
+ "\n type : "
+ ((types[i] == QLCore.Option.Type.Put) ? "Put" : "Call"));
}
}
}
}
}
public void testSpuriousOscillations()
{
//Testing for spurious oscillations when solving the Heston PDEs...
using (SavedSettings backup = new SavedSettings())
{
DayCounter dc = new Actual365Fixed();
Date today = new Date(7, 6, 2018);
Settings.Instance.setEvaluationDate(today);
Handle <Quote> spot = new Handle <Quote>(new SimpleQuote(100.0));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.1, dc));
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.0, dc));
double v0 = 0.005;
double kappa = 1.0;
double theta = 0.005;
double sigma = 0.4;
double rho = -0.75;
Date maturity = today + new Period(1, TimeUnit.Years);
HestonProcess process =
new HestonProcess(
rTS, qTS, spot, v0, kappa, theta, sigma, rho);
HestonModel model =
new HestonModel(process);
FdHestonVanillaEngine hestonEngine =
new FdHestonVanillaEngine(
model, 6, 200, 13, 0, new FdmSchemeDesc().TrBDF2());
VanillaOption option = new VanillaOption(new PlainVanillaPayoff(Option.Type.Call, spot.currentLink().value()),
new EuropeanExercise(maturity));
option.setupArguments(hestonEngine.getArguments());
List <Tuple <FdmSchemeDesc, string, bool> > descs = new List <Tuple <FdmSchemeDesc, string, bool> >();
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().CraigSneyd(), "Craig-Sneyd", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().Hundsdorfer(), "Hundsdorfer", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().ModifiedHundsdorfer(), "Mod. Hundsdorfer", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().Douglas(), "Douglas", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().CrankNicolson(), "Crank-Nicolson", true));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().ImplicitEuler(), "Implicit", false));
descs.Add(new Tuple <FdmSchemeDesc, string, bool>(new FdmSchemeDesc().TrBDF2(), "TR-BDF2", false));
for (int j = 0; j < descs.Count; ++j)
{
FdmHestonSolver solver =
new FdmHestonSolver(new Handle <HestonProcess>(process),
hestonEngine.getSolverDesc(1.0),
descs[j].Item1);
List <double> gammas = new List <double>();
for (double x = 99; x < 101.001; x += 0.1)
{
gammas.Add(solver.gammaAt(x, v0));
}
double maximum = Double.MinValue;
for (int i = 1; i < gammas.Count; ++i)
{
double diff = Math.Abs(gammas[i] - gammas[i - 1]);
if (diff > maximum)
{
maximum = diff;
}
}
double tol = 0.01;
bool hasSpuriousOscillations = maximum > tol;
if (hasSpuriousOscillations != descs[j].Item3)
{
QAssert.Fail("unable to reproduce spurious oscillation behaviour "
+ "\n scheme name : " + descs[j].Item2
+ "\n oscillations observed: "
+ hasSpuriousOscillations
+ "\n oscillations expected: " + descs[j].Item3
);
}
}
}
}
public AnalyticHestonEngine(HestonModel model) : this(NQuantLibcPINVOKE.new_AnalyticHestonEngine__SWIG_1(HestonModel.getCPtr(model)), true) {
if (NQuantLibcPINVOKE.SWIGPendingException.Pending) throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(HestonModel obj) {
return (obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr;
}
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 AnalyticHestonEngine(HestonModel model, double relTolerance, uint maxEvaluations) : this(NQuantLibcPINVOKE.new_AnalyticHestonEngine__SWIG_2(HestonModel.getCPtr(model), relTolerance, maxEvaluations), true) {
if (NQuantLibcPINVOKE.SWIGPendingException.Pending) throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
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);
}
}
}
