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]);
}
}
}
}