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
);
}
}
}
}