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);
}
}
}
}
/*! This method checks whether the asset was rolled at the given time. */
protected bool isOnTime(double t)
{
TimeGrid grid = method().timeGrid();
return(Utils.close(grid[grid.index(t)], time()));
}
public void testSwaptionPricing()
{
//"Testing forward swap and swaption pricing...");
//SavedSettings backup;
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 ,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)
Assert.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<MultiPath> path = (n%2!=0) ? generator.antithetic()
: generator.next();
//Sample<MultiPath> path = generator.next();
List<double> rates_ = new InitializedList<double>(size);
for (int k=0; k<process.size(); ++k) {
rates_[k] = path.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)
Assert.Fail("Failed to reproduce swaption npv"
+ "\n calculated: " + stat.mean()
+ "\n expected: " + swaption.NPV());
}
}
}
}
