public void testSwaptionPricing()
{
// Testing forward swap and swaption pricing
const int size = 10;
const int steps = 8 * size;
#if QL_USE_INDEXED_COUPON
const double tolerance = 1e-6;
#else
const double tolerance = 1e-12;
#endif
List <Date> dates = new List <Date>();
List <double> rates = new List <double>();
dates.Add(new Date(4, 9, 2005));
dates.Add(new Date(4, 9, 2011));
rates.Add(0.04);
rates.Add(0.08);
IborIndex index = makeIndex(dates, rates);
LiborForwardModelProcess process = new LiborForwardModelProcess(size, index);
LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.5);
LmVolatilityModel volaModel = new LmLinearExponentialVolatilityModel(process.fixingTimes(),
0.291, 1.483, 0.116, 0.00001);
// set-up pricing engine
process.setCovarParam((LfmCovarianceParameterization)
new LfmCovarianceProxy(volaModel, corrModel));
// set-up a small Monte-Carlo simulation to price swations
List <double> tmp = process.fixingTimes();
TimeGrid grid = new TimeGrid(tmp, tmp.Count, steps);
List <int> location = new List <int>();
for (int i = 0; i < tmp.Count; ++i)
{
location.Add(grid.index(tmp[i]));
}
ulong seed = 42;
const int nrTrails = 5000;
LowDiscrepancy.icInstance = new InverseCumulativeNormal();
IRNG rsg = (InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng>
, InverseCumulativeNormal>)
new PseudoRandom().make_sequence_generator(process.factors() * (grid.size() - 1), seed);
MultiPathGenerator <IRNG> generator = new MultiPathGenerator <IRNG>(process,
grid,
rsg, false);
LiborForwardModel liborModel = new LiborForwardModel(process, volaModel, corrModel);
Calendar calendar = index.fixingCalendar();
DayCounter dayCounter = index.forwardingTermStructure().link.dayCounter();
BusinessDayConvention convention = index.businessDayConvention();
Date settlement = index.forwardingTermStructure().link.referenceDate();
SwaptionVolatilityMatrix m = liborModel.getSwaptionVolatilityMatrix();
for (int i = 1; i < size; ++i)
{
for (int j = 1; j <= size - i; ++j)
{
Date fwdStart = settlement + new Period(6 * i, TimeUnit.Months);
Date fwdMaturity = fwdStart + new Period(6 * j, TimeUnit.Months);
Schedule schedule = new Schedule(fwdStart, fwdMaturity, index.tenor(), calendar,
convention, convention, DateGeneration.Rule.Forward, false);
double swapRate = 0.0404;
VanillaSwap forwardSwap = new VanillaSwap(VanillaSwap.Type.Receiver, 1.0,
schedule, swapRate, dayCounter,
schedule, index, 0.0, index.dayCounter());
forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure()));
// check forward pricing first
double expected = forwardSwap.fairRate();
double calculated = liborModel.S_0(i - 1, i + j - 1);
if (Math.Abs(expected - calculated) > tolerance)
{
QAssert.Fail("Failed to reproduce fair forward swap rate"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
swapRate = forwardSwap.fairRate();
forwardSwap =
new VanillaSwap(VanillaSwap.Type.Receiver, 1.0,
schedule, swapRate, dayCounter,
schedule, index, 0.0, index.dayCounter());
forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure()));
if (i == j && i <= size / 2)
{
IPricingEngine engine =
new LfmSwaptionEngine(liborModel, index.forwardingTermStructure());
Exercise exercise =
new EuropeanExercise(process.fixingDates()[i]);
Swaption swaption =
new Swaption(forwardSwap, exercise);
swaption.setPricingEngine(engine);
GeneralStatistics stat = new GeneralStatistics();
for (int n = 0; n < nrTrails; ++n)
{
Sample <IPath> path = (n % 2 != 0) ? generator.antithetic()
: generator.next();
MultiPath value = path.value as MultiPath;
Utils.QL_REQUIRE(value != null, () => "Invalid Path");
//Sample<MultiPath> path = generator.next();
List <double> rates_ = new InitializedList <double>(size);
for (int k = 0; k < process.size(); ++k)
{
rates_[k] = value[k][location[i]];
}
List <double> dis = process.discountBond(rates_);
double npv = 0.0;
for (int k = i; k < i + j; ++k)
{
npv += (swapRate - rates_[k])
* (process.accrualEndTimes()[k]
- process.accrualStartTimes()[k]) * dis[k];
}
stat.add(Math.Max(npv, 0.0));
}
if (Math.Abs(swaption.NPV() - stat.mean())
> stat.errorEstimate() * 2.35)
{
QAssert.Fail("Failed to reproduce swaption npv"
+ "\n calculated: " + stat.mean()
+ "\n expected: " + swaption.NPV());
}
}
}
}
}
public void testCallableEquityPricing()
{
// Testing the pricing of a callable equity product
/*
* For the definition of the example product see
* Alexander Giese, On the Pricing of Auto-Callable Equity
* Structures in the Presence of Stochastic Volatility and
* Stochastic Interest Rates .
* http://workshop.mathfinance.de/2006/papers/giese/slides.pdf
*/
int maturity = 7;
DayCounter dc = new Actual365Fixed();
Date today = Date.Today;
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(0.04);
Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, rRate, dc));
HestonProcess hestonProcess = new HestonProcess(rTS, qTS, spot, 0.0625, 1.0, 0.24 * 0.24, 1e-4, 0.0);
// FLOATING_POINT_EXCEPTION
HullWhiteForwardProcess hwProcess = new HullWhiteForwardProcess(rTS, 0.00883, 0.00526);
hwProcess.setForwardMeasureTime(dc.yearFraction(today, today + new Period(maturity + 1, TimeUnit.Years)));
HybridHestonHullWhiteProcess jointProcess = new HybridHestonHullWhiteProcess(hestonProcess, hwProcess, -0.4);
Schedule schedule = new Schedule(today, today + new Period(maturity, TimeUnit.Years), new Period(1, TimeUnit.Years),
new TARGET(), BusinessDayConvention.Following, BusinessDayConvention.Following, DateGeneration.Rule.Forward, false);
List <double> times = new InitializedList <double>(maturity + 1);
for (int i = 0; i <= maturity; ++i)
{
times[i] = i;
}
TimeGrid grid = new TimeGrid(times, times.Count);
List <double> redemption = new InitializedList <double>(maturity);
for (int i = 0; i < maturity; ++i)
{
redemption[i] = 1.07 + 0.03 * i;
}
ulong seed = 42;
IRNG rsg = (InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng>
, InverseCumulativeNormal>)
new PseudoRandom().make_sequence_generator(jointProcess.factors() * (grid.size() - 1), seed);
MultiPathGenerator <IRNG> generator = new MultiPathGenerator <IRNG>(jointProcess, grid, rsg, false);
GeneralStatistics stat = new GeneralStatistics();
double antitheticPayoff = 0;
int nrTrails = 40000;
for (int i = 0; i < nrTrails; ++i)
{
bool antithetic = (i % 2) != 0;
Sample <IPath> path = antithetic ? generator.antithetic() : generator.next();
MultiPath value = path.value as MultiPath;
Utils.QL_REQUIRE(value != null, () => "Invalid Path");
double payoff = 0;
for (int j = 1; j <= maturity; ++j)
{
if (value[0][j] > spot.link.value())
{
Vector states = new Vector(3);
for (int k = 0; k < 3; ++k)
{
states[k] = value[k][j];
}
payoff = redemption[j - 1] / jointProcess.numeraire(grid[j], states);
break;
}
else if (j == maturity)
{
Vector states = new Vector(3);
for (int k = 0; k < 3; ++k)
{
states[k] = value[k][j];
}
payoff = 1.0 / jointProcess.numeraire(grid[j], states);
}
}
if (antithetic)
{
stat.add(0.5 * (antitheticPayoff + payoff));
}
else
{
antitheticPayoff = payoff;
}
}
double expected = 0.938;
double calculated = stat.mean();
double error = stat.errorEstimate();
if (Math.Abs(expected - calculated) > 3 * error)
{
QAssert.Fail("Failed to reproduce auto-callable equity structure price"
+ "\n calculated: " + calculated
+ "\n error: " + error
+ "\n expected: " + expected);
}
}