public void testFdmHestonEuropeanWithDividends()
{
//Testing FDM with European option with dividends in Heston model...
using (SavedSettings backup = new SavedSettings())
{
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(100.0));
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.05, new Actual365Fixed()));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.0, new Actual365Fixed()));
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, s0, 0.04, 2.5, 0.04, 0.66, -0.8);
Settings.Instance.setEvaluationDate(new Date(28, 3, 2004));
Date exerciseDate = new Date(28, 3, 2005);
Exercise exercise = new AmericanExercise(exerciseDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, 100);
List <double> dividends = new InitializedList <double>(1, 5);
List <Date> dividendDates = new InitializedList <Date>(1, new Date(28, 9, 2004));
DividendVanillaOption option = new DividendVanillaOption(payoff, exercise, dividendDates, dividends);
IPricingEngine engine = new FdHestonVanillaEngine(new HestonModel(hestonProcess), 50, 100, 50);
option.setPricingEngine(engine);
double tol = 0.01;
double gammaTol = 0.001;
double npvExpected = 7.365075;
double deltaExpected = -0.396678;
double gammaExpected = 0.027681;
if (Math.Abs(option.NPV() - npvExpected) > tol)
{
QAssert.Fail("Failed to reproduce expected npv"
+ "\n calculated: " + option.NPV()
+ "\n expected: " + npvExpected
+ "\n tolerance: " + tol);
}
if (Math.Abs(option.delta() - deltaExpected) > tol)
{
QAssert.Fail("Failed to reproduce expected delta"
+ "\n calculated: " + option.delta()
+ "\n expected: " + deltaExpected
+ "\n tolerance: " + tol);
}
if (Math.Abs(option.gamma() - gammaExpected) > gammaTol)
{
QAssert.Fail("Failed to reproduce expected gamma"
+ "\n calculated: " + option.gamma()
+ "\n expected: " + gammaExpected
+ "\n tolerance: " + tol);
}
}
}
public void testFdmHestonIkonenToivanen()
{
//Testing FDM Heston for Ikonen and Toivanen tests...
/* check prices of american puts as given in:
* From Efficient numerical methods for pricing American options under
* stochastic volatility, Samuli Ikonen, Jari Toivanen,
* http://users.jyu.fi/~tene/papers/reportB12-05.pdf
*/
using (SavedSettings backup = new SavedSettings())
{
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.10, new Actual360()));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(0.0, new Actual360()));
Settings.Instance.setEvaluationDate(new Date(28, 3, 2004));
Date exerciseDate = new Date(26, 6, 2004);
Exercise exercise = new AmericanExercise(exerciseDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, 10);
VanillaOption option = new VanillaOption(payoff, exercise);
double[] strikes = new double[] { 8, 9, 10, 11, 12 };
double[] expected = new double[] { 2.00000, 1.10763, 0.520038, 0.213681, 0.082046 };
double tol = 0.001;
for (int i = 0; i < strikes.Length; ++i)
{
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(strikes[i]));
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, s0, 0.0625, 5, 0.16, 0.9, 0.1);
IPricingEngine engine = new FdHestonVanillaEngine(new HestonModel(hestonProcess), 100, 400);
option.setPricingEngine(engine);
double calculated = option.NPV();
if (Math.Abs(calculated - expected[i]) > tol)
{
QAssert.Fail("Failed to reproduce expected npv"
+ "\n strike: " + strikes[i]
+ "\n calculated: " + calculated
+ "\n expected: " + expected[i]
+ "\n tolerance: " + tol);
}
}
}
}
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 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);
}
}
}
public void testFdmHestonConvergence()
{
/* convergence tests based on
* ADI finite difference schemes for option pricing in the
* Heston model with correlation, K.J. in t'Hout and S. Foulon
*/
//Testing FDM Heston convergence...
using (SavedSettings backup = new SavedSettings())
{
HestonTestData[] values = new HestonTestData[] {
new HestonTestData(1.5, 0.04, 0.3, -0.9, 0.025, 0.0, 1.0, 100),
new HestonTestData(3.0, 0.12, 0.04, 0.6, 0.01, 0.04, 1.0, 100),
new HestonTestData(0.6067, 0.0707, 0.2928, -0.7571, 0.03, 0.0, 3.0, 100),
new HestonTestData(2.5, 0.06, 0.5, -0.1, 0.0507, 0.0469, 0.25, 100)
};
FdmSchemeDesc[] schemes = new FdmSchemeDesc[] {
new FdmSchemeDesc().Hundsdorfer(),
new FdmSchemeDesc().ModifiedCraigSneyd(),
new FdmSchemeDesc().ModifiedHundsdorfer(),
new FdmSchemeDesc().CraigSneyd(),
new FdmSchemeDesc().TrBDF2(),
new FdmSchemeDesc().CrankNicolson(),
};
int[] tn = new int[] { 60 };
double[] v0 = new double[] { 0.04 };
Date todaysDate = new Date(28, 3, 2004);
Settings.Instance.setEvaluationDate(todaysDate);
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(75.0));
for (int l = 0; l < schemes.Length; ++l)
{
for (int i = 0; i < values.Length; ++i)
{
for (int j = 0; j < tn.Length; ++j)
{
for (int k = 0; k < v0.Length; ++k)
{
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(
Utilities.flatRate(values[i].r, new Actual365Fixed()));
Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(
Utilities.flatRate(values[i].q, new Actual365Fixed()));
HestonProcess hestonProcess =
new HestonProcess(rTS, qTS, s0,
v0[k],
values[i].kappa,
values[i].theta,
values[i].sigma,
values[i].rho);
Date exerciseDate = todaysDate
+ new Period(Convert.ToInt32(values[i].T * 365), TimeUnit.Days);
Exercise exercise = new EuropeanExercise(exerciseDate);
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Call, values[i].K);
VanillaOption option = new VanillaOption(payoff, exercise);
IPricingEngine engine =
new FdHestonVanillaEngine(
new HestonModel(hestonProcess),
tn[j], 101, 51, 0,
schemes[l]);
option.setPricingEngine(engine);
double calculated = option.NPV();
IPricingEngine analyticEngine =
new AnalyticHestonEngine(
new HestonModel(hestonProcess), 144);
option.setPricingEngine(analyticEngine);
double expected = option.NPV();
if (Math.Abs(expected - calculated) / expected > 0.02 &&
Math.Abs(expected - calculated) > 0.002)
{
QAssert.Fail("Failed to reproduce expected npv"
+ "\n calculated: " + calculated
+ "\n expected: " + expected
+ "\n tolerance: " + 0.01);
}
}
}
}
}
}
}
internal static global::System.Runtime.InteropServices.HandleRef getCPtr(FdHestonVanillaEngine obj)
{
return((obj == null) ? new global::System.Runtime.InteropServices.HandleRef(null, global::System.IntPtr.Zero) : obj.swigCPtr);
}