public void testZeroBondPricing()
{
// Testing Monte-Carlo zero bond 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>();
dates.Add(today);
rates.Add(0.02);
times.Add(0.0);
for (int i = 120; i < 240; ++i)
{
dates.Add(today + new Period(i, TimeUnit.Months));
rates.Add(0.02 + 0.0002 * Math.Exp(Math.Sin(i / 8.0)));
times.Add(dc.yearFraction(today, dates.Last()));
}
Date maturity = dates.Last() + new Period(10, TimeUnit.Years);
dates.Add(maturity);
rates.Add(0.04);
//times.Add(dc.yearFraction(today, dates.Last()));
Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(100));
Handle <YieldTermStructure> ts = new Handle <YieldTermStructure>(new InterpolatedZeroCurve <Linear>(dates, rates, dc));
Handle <YieldTermStructure> ds = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.0, dc));
HestonProcess hestonProcess = new HestonProcess(ts, ds, s0, 0.02, 1.0, 0.2, 0.5, -0.8);
HullWhiteForwardProcess hwProcess = new HullWhiteForwardProcess(ts, 0.05, 0.05);
hwProcess.setForwardMeasureTime(dc.yearFraction(today, maturity));
HullWhite hwModel = new HullWhite(ts, 0.05, 0.05);
HybridHestonHullWhiteProcess jointProcess = new HybridHestonHullWhiteProcess(hestonProcess, hwProcess, -0.4);
TimeGrid grid = new TimeGrid(times);
int factors = jointProcess.factors();
int steps = grid.size() - 1;
SobolBrownianBridgeRsg rsg = new SobolBrownianBridgeRsg(factors, steps);
MultiPathGenerator <SobolBrownianBridgeRsg> generator = new MultiPathGenerator <SobolBrownianBridgeRsg>(
jointProcess, grid, rsg, false);
int m = 90;
List <GeneralStatistics> zeroStat = new InitializedList <GeneralStatistics>(m);
List <GeneralStatistics> optionStat = new InitializedList <GeneralStatistics>(m);
int nrTrails = 8191;
int optionTenor = 24;
double strike = 0.5;
for (int i = 0; i < nrTrails; ++i)
{
Sample <IPath> path = generator.next();
MultiPath value = path.value as MultiPath;
Utils.QL_REQUIRE(value != null, () => "Invalid Path");
for (int j = 1; j < m; ++j)
{
double t = grid[j]; // zero end and option maturity
double T = grid[j + optionTenor]; // maturity of zero bond
// of option
Vector states = new Vector(3);
Vector optionStates = new Vector(3);
for (int k = 0; k < jointProcess.size(); ++k)
{
states[k] = value[k][j];
optionStates[k] = value[k][j + optionTenor];
}
double zeroBond
= 1.0 / jointProcess.numeraire(t, states);
double zeroOption = zeroBond * Math.Max(0.0, hwModel.discountBond(t, T, states[2]) - strike);
zeroStat[j].add(zeroBond);
optionStat[j].add(zeroOption);
}
}
for (int j = 1; j < m; ++j)
{
double t = grid[j];
double calculated = zeroStat[j].mean();
double expected = ts.link.discount(t);
if (Math.Abs(calculated - expected) > 0.03)
{
QAssert.Fail("Failed to reproduce expected zero bond prices"
+ "\n t: " + t
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
double T = grid[j + optionTenor];
calculated = optionStat[j].mean();
expected = hwModel.discountBondOption(Option.Type.Call, strike, t, T);
if (Math.Abs(calculated - expected) > 0.0035)
{
QAssert.Fail("Failed to reproduce expected zero bond option prices"
+ "\n t: " + t
+ "\n T: " + T
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
}
}
