public void testBsmHullWhiteEngine()
{
// Testing European option pricing for a BSM process with one-factor Hull-White model
DayCounter dc = new Actual365Fixed();
Date today = Date.Today;
Date maturity = today + new Period(20, TimeUnit.Years);
Settings.Instance.setEvaluationDate(today);
Handle <Quote> spot = new Handle <Quote>(new SimpleQuote(100.0));
SimpleQuote qRate = new SimpleQuote(0.04);
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, qRate, dc));
SimpleQuote rRate = new SimpleQuote(0.0525);
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, rRate, dc));
SimpleQuote vol = new SimpleQuote(0.25);
Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(Utilities.flatVol(today, vol, dc));
// FLOATING_POINT_EXCEPTION
HullWhite hullWhiteModel = new HullWhite(new Handle <YieldTermStructure>(rTS), 0.00883, 0.00526);
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(spot, qTS, rTS, volTS);
Exercise exercise = new EuropeanExercise(maturity);
double fwd = spot.link.value() * qTS.link.discount(maturity) / rTS.link.discount(maturity);
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Call, fwd);
EuropeanOption option = new EuropeanOption(payoff, exercise);
double tol = 1e-8;
double[] corr = { -0.75, -0.25, 0.0, 0.25, 0.75 };
double[] expectedVol = { 0.217064577, 0.243995801, 0.256402830, 0.268236596, 0.290461343 };
for (int i = 0; i < corr.Length; ++i)
{
IPricingEngine bsmhwEngine = new AnalyticBSMHullWhiteEngine(corr[i], stochProcess, hullWhiteModel);
option.setPricingEngine(bsmhwEngine);
double npv = option.NPV();
Handle <BlackVolTermStructure> compVolTS = new Handle <BlackVolTermStructure>(
Utilities.flatVol(today, expectedVol[i], dc));
BlackScholesMertonProcess bsProcess = new BlackScholesMertonProcess(spot, qTS, rTS, compVolTS);
IPricingEngine bsEngine = new AnalyticEuropeanEngine(bsProcess);
EuropeanOption comp = new EuropeanOption(payoff, exercise);
comp.setPricingEngine(bsEngine);
double impliedVol = comp.impliedVolatility(npv, bsProcess, 1e-10, 100);
if (Math.Abs(impliedVol - expectedVol[i]) > tol)
{
QAssert.Fail("Failed to reproduce implied volatility"
+ "\n calculated: " + impliedVol
+ "\n expected : " + expectedVol[i]);
}
if (Math.Abs((comp.NPV() - npv) / npv) > tol)
{
QAssert.Fail("Failed to reproduce NPV"
+ "\n calculated: " + npv
+ "\n expected : " + comp.NPV());
}
if (Math.Abs(comp.delta() - option.delta()) > tol)
{
QAssert.Fail("Failed to reproduce NPV"
+ "\n calculated: " + npv
+ "\n expected : " + comp.NPV());
}
if (Math.Abs((comp.gamma() - option.gamma()) / npv) > tol)
{
QAssert.Fail("Failed to reproduce NPV"
+ "\n calculated: " + npv
+ "\n expected : " + comp.NPV());
}
if (Math.Abs((comp.theta() - option.theta()) / npv) > tol)
{
QAssert.Fail("Failed to reproduce NPV"
+ "\n calculated: " + npv
+ "\n expected : " + comp.NPV());
}
if (Math.Abs((comp.vega() - option.vega()) / npv) > tol)
{
QAssert.Fail("Failed to reproduce NPV"
+ "\n calculated: " + npv
+ "\n expected : " + comp.NPV());
}
}
}
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"));
}
}
}
}
}
