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 testMonteCarloCapletPricing()
{
//"Testing caplet LMM Monte-Carlo caplet pricing..."
//SavedSettings backup;
/* factor loadings are taken from Hull & White article
* plus extra normalisation to get orthogonal eigenvectors
* http://www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf */
double[] compValues = { 0.85549771, 0.46707264, 0.22353259,
0.91915359, 0.37716089, 0.11360610,
0.96438280, 0.26413316, -0.01412414,
0.97939148, 0.13492952, -0.15028753,
0.95970595, -0.00000000, -0.28100621,
0.97939148, -0.13492952, -0.15028753,
0.96438280, -0.26413316, -0.01412414,
0.91915359, -0.37716089, 0.11360610,
0.85549771, -0.46707264, 0.22353259 };
Matrix volaComp = new Matrix(9, 3);
List <double> lcompValues = new InitializedList <double>(27, 0);
List <double> ltemp = new InitializedList <double>(3, 0);
lcompValues = compValues.ToList();
//std::copy(compValues, compValues+9*3, volaComp.begin());
for (int i = 0; i < 9; i++)
{
ltemp = lcompValues.GetRange(3 * i, 3);
for (int j = 0; j < 3; j++)
{
volaComp[i, j] = ltemp[j];
}
}
LiborForwardModelProcess process1 = makeProcess();
LiborForwardModelProcess process2 = makeProcess(volaComp);
List <double> tmp = process1.fixingTimes();
TimeGrid grid = new TimeGrid(tmp, 12);
List <int> location = new List <int>();
for (int i = 0; i < tmp.Count; ++i)
{
location.Add(grid.index(tmp[i]));
}
// set-up a small Monte-Carlo simulation to price caplets
// and ratchet caps using a one- and a three factor libor market model
ulong seed = 42;
LowDiscrepancy.icInstance = new InverseCumulativeNormal();
IRNG rsg1 = (IRNG) new LowDiscrepancy().make_sequence_generator(
process1.factors() * (grid.size() - 1), seed);
IRNG rsg2 = (IRNG) new LowDiscrepancy().make_sequence_generator(
process2.factors() * (grid.size() - 1), seed);
MultiPathGenerator <IRNG> generator1 = new MultiPathGenerator <IRNG> (process1, grid, rsg1, false);
MultiPathGenerator <IRNG> generator2 = new MultiPathGenerator <IRNG> (process2, grid, rsg2, false);
const int nrTrails = 250000;
List <GeneralStatistics> stat1 = new InitializedList <GeneralStatistics>(process1.size());
List <GeneralStatistics> stat2 = new InitializedList <GeneralStatistics>(process2.size());
List <GeneralStatistics> stat3 = new InitializedList <GeneralStatistics>(process2.size() - 1);
for (int i = 0; i < nrTrails; ++i)
{
Sample <MultiPath> path1 = generator1.next();
Sample <MultiPath> path2 = generator2.next();
List <double> rates1 = new InitializedList <double>(len);
List <double> rates2 = new InitializedList <double>(len);
for (int j = 0; j < process1.size(); ++j)
{
rates1[j] = path1.value[j][location[j]];
rates2[j] = path2.value[j][location[j]];
}
List <double> dis1 = process1.discountBond(rates1);
List <double> dis2 = process2.discountBond(rates2);
for (int k = 0; k < process1.size(); ++k)
{
double accrualPeriod = process1.accrualEndTimes()[k]
- process1.accrualStartTimes()[k];
// caplet payoff function, cap rate at 4%
double payoff1 = Math.Max(rates1[k] - 0.04, 0.0) * accrualPeriod;
double payoff2 = Math.Max(rates2[k] - 0.04, 0.0) * accrualPeriod;
stat1[k].add(dis1[k] * payoff1);
stat2[k].add(dis2[k] * payoff2);
if (k != 0)
{
// ratchet cap payoff function
double payoff3 = Math.Max(rates2[k] - (rates2[k - 1] + 0.0025), 0.0)
* accrualPeriod;
stat3[k - 1].add(dis2[k] * payoff3);
}
}
}
double[] capletNpv = { 0.000000000000, 0.000002841629, 0.002533279333,
0.009577143571, 0.017746502618, 0.025216116835,
0.031608230268, 0.036645683881, 0.039792254012,
0.041829864365 };
double[] ratchetNpv = { 0.0082644895, 0.0082754754, 0.0082159966,
0.0082982822, 0.0083803357, 0.0084366961,
0.0084173270, 0.0081803406, 0.0079533814 };
for (int k = 0; k < process1.size(); ++k)
{
double calculated1 = stat1[k].mean();
double tolerance1 = stat1[k].errorEstimate();
double expected = capletNpv[k];
if (Math.Abs(calculated1 - expected) > tolerance1)
{
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated1
+ "\n error int: " + tolerance1
+ "\n expected: " + expected);
}
double calculated2 = stat2[k].mean();
double tolerance2 = stat2[k].errorEstimate();
if (Math.Abs(calculated2 - expected) > tolerance2)
{
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated2
+ "\n error int: " + tolerance2
+ "\n expected: " + expected);
}
if (k != 0)
{
double calculated3 = stat3[k - 1].mean();
double tolerance3 = stat3[k - 1].errorEstimate();
expected = ratchetNpv[k - 1];
double refError = 1e-5; // 1e-5. error bars of the reference values
if (Math.Abs(calculated3 - expected) > tolerance3 + refError)
{
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated3
+ "\n error int: " + tolerance3 + refError
+ "\n expected: " + expected);
}
}
}
}