OptionletVolatilityStructure makeCapVolCurve(Date todaysDate)
{
double[] vols = {14.40, 17.15, 16.81, 16.64, 16.17,
15.78, 15.40, 15.21, 14.86};
List<Date> dates=new List<Date>() ;
List<double> capletVols=new List<double>();
LiborForwardModelProcess process=
new LiborForwardModelProcess(10, makeIndex());
for (int i=0; i < 9; ++i) {
capletVols.Add(vols[i]/100);
dates.Add(process.fixingDates()[i+1]);
}
return new CapletVarianceCurve(todaysDate, dates,
capletVols,new Actual360());
}
// calculating swaption volatility matrix using
// Rebonatos approx. formula. Be aware that this
// matrix is valid only for regular fixings and
// assumes that the fix and floating leg have the
// same frequency
public SwaptionVolatilityMatrix getSwaptionVolatilityMatrix()
{
if (swaptionVola != null)
{
return(swaptionVola);
}
IborIndex index = process_.index();
Date today = process_.fixingDates()[0];
int size = process_.size() / 2;
Matrix volatilities = new Matrix(size, size);
List <Date> exercises = new InitializedList <Date>(size);
for (int i = 0; i < size; ++i)
{
exercises[i] = process_.fixingDates()[i + 1];
}
List <Period> lengths = new InitializedList <Period>(size);
for (int i = 0; i < size; ++i)
{
lengths[i] = (i + 1) * index.tenor();
}
Vector f = process_.initialValues();
for (int k = 0; k < size; ++k)
{
int alpha = k;
double t_alpha = process_.fixingTimes()[alpha + 1];
Matrix var = new Matrix(size, size);
for (int i = alpha + 1; i <= k + size; ++i)
{
for (int j = i; j <= k + size; ++j)
{
var[i - alpha - 1, j - alpha - 1] = var[j - alpha - 1, i - alpha - 1] =
covarProxy_.integratedCovariance(i, j, t_alpha, null);
}
}
for (int l = 1; l <= size; ++l)
{
int beta = l + k;
Vector w = w_0(alpha, beta);
double sum = 0.0;
for (int i = alpha + 1; i <= beta; ++i)
{
for (int j = alpha + 1; j <= beta; ++j)
{
sum += w[i] * w[j] * f[i] * f[j] * var[i - alpha - 1, j - alpha - 1];
}
}
volatilities[k, l - 1] =
Math.Sqrt(sum / t_alpha) / S_0(alpha, beta);
}
}
return(swaptionVola = new SwaptionVolatilityMatrix(today, exercises, lengths,
volatilities, index.dayCounter()));
}
CapletVarianceCurve makeCapVolCurve(Date todaysDate)
{
double[] vols = {14.40, 17.15, 16.81, 16.64, 16.17,
15.78, 15.40, 15.21, 14.86, 14.54};
List<Date> dates = new List<Date>();
List<double> capletVols = new List<double>();
LiborForwardModelProcess process= new LiborForwardModelProcess(len+1, makeIndex(),null);
for (int i=0; i < len; ++i)
{
capletVols.Add(vols[i]/100);
dates.Add(process.fixingDates()[i+1]);
}
return new CapletVarianceCurve( todaysDate, dates,
capletVols, new ActualActual());
}
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());
}
}
}
}
public LfmHullWhiteParameterization(
LiborForwardModelProcess process,
OptionletVolatilityStructure capletVol,
Matrix correlation, int factors)
: base(process.size(), factors)
{
diffusion_ = new Matrix(size_ - 1, factors_);
fixingTimes_ = process.fixingTimes();
Matrix sqrtCorr = new Matrix(size_ - 1, factors_, 1.0);
if (correlation.empty())
{
if (!(factors_ == 1))
{
throw new ApplicationException("correlation matrix must be given for " +
"multi factor models");
}
}
else
{
if (!(correlation.rows() == size_ - 1 &&
correlation.rows() == correlation.columns()))
{
throw new ApplicationException("wrong dimesion of the correlation matrix");
}
if (!(factors_ <= size_ - 1))
{
throw new ApplicationException("too many factors for given LFM process");
}
Matrix tmpSqrtCorr = MatrixUtilitites.pseudoSqrt(correlation,
MatrixUtilitites.SalvagingAlgorithm.Spectral);
// reduce to n factor model
// "Reconstructing a valid correlation matrix from invalid data"
// (<http://www.quarchome.org/correlationmatrix.pdf>)
for (int i = 0; i < size_ - 1; ++i)
{
double d = 0;
tmpSqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => d += vv * tmpSqrtCorr.row(i)[ii]);
//sqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => sqrtCorr.row(i)[ii] = tmpSqrtCorr.row(i).GetRange(0, factors_)[ii] / Math.Sqrt(d));
for (int k = 0; k < factors_; ++k)
{
sqrtCorr[i, k] = tmpSqrtCorr.row(i).GetRange(0, factors_)[k] / Math.Sqrt(d);
}
}
}
List <double> lambda = new List <double>();
DayCounter dayCounter = process.index().dayCounter();
List <double> fixingTimes = process.fixingTimes();
List <Date> fixingDates = process.fixingDates();
for (int i = 1; i < size_; ++i)
{
double cumVar = 0.0;
for (int j = 1; j < i; ++j)
{
cumVar += lambda[i - j - 1] * lambda[i - j - 1]
* (fixingTimes[j + 1] - fixingTimes[j]);
}
double vol = capletVol.volatility(fixingDates[i], 0.0, false);
double var = vol * vol
* capletVol.dayCounter().yearFraction(fixingDates[0],
fixingDates[i]);
lambda.Add(Math.Sqrt((var - cumVar)
/ (fixingTimes[1] - fixingTimes[0])));
for (int q = 0; q < factors_; ++q)
{
diffusion_[i - 1, q] = sqrtCorr[i - 1, q] * lambda.Last();
}
}
covariance_ = diffusion_ * Matrix.transpose(diffusion_);
}
public LfmHullWhiteParameterization(
LiborForwardModelProcess process,
OptionletVolatilityStructure capletVol,
Matrix correlation, int factors)
: base(process.size(), factors)
{
diffusion_ = new Matrix(size_-1, factors_);
fixingTimes_= process.fixingTimes();
Matrix sqrtCorr = new Matrix(size_ - 1, factors_, 1.0);
if (correlation.empty()) {
if(!(factors_ == 1))
throw new ApplicationException("correlation matrix must be given for "+
"multi factor models");
} else {
if(!(correlation.rows() == size_-1
&& correlation.rows() == correlation.columns()))
throw new ApplicationException("wrong dimesion of the correlation matrix");
if(!(factors_ <= size_-1))
throw new ApplicationException("too many factors for given LFM process");
Matrix tmpSqrtCorr =MatrixUtilitites.pseudoSqrt(correlation,
MatrixUtilitites.SalvagingAlgorithm.Spectral);
// reduce to n factor model
// "Reconstructing a valid correlation matrix from invalid data"
// (<http://www.quarchome.org/correlationmatrix.pdf>)
for (int i=0; i < size_-1; ++i) {
double d = 0;
tmpSqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => d += vv*tmpSqrtCorr.row(i)[ii]);
//sqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => sqrtCorr.row(i)[ii] = tmpSqrtCorr.row(i).GetRange(0, factors_)[ii] / Math.Sqrt(d));
for (int k = 0; k < factors_; ++k){
sqrtCorr[i, k] = tmpSqrtCorr.row(i).GetRange(0, factors_)[k] / Math.Sqrt(d);
}
}
}
List<double> lambda=new List<double>();
DayCounter dayCounter = process.index().dayCounter();
List<double> fixingTimes = process.fixingTimes();
List<Date> fixingDates = process.fixingDates();
for (int i = 1; i < size_; ++i) {
double cumVar = 0.0;
for (int j = 1; j < i; ++j) {
cumVar += lambda[i-j-1] * lambda[i-j-1]
* (fixingTimes[j+1] - fixingTimes[j]);
}
double vol = capletVol.volatility(fixingDates[i], 0.0,false);
double var = vol * vol
* capletVol.dayCounter().yearFraction(fixingDates[0],
fixingDates[i]);
lambda.Add(Math.Sqrt( (var - cumVar)
/ (fixingTimes[1] - fixingTimes[0])) );
for (int q=0; q<factors_; ++q) {
diffusion_[i - 1, q]=sqrtCorr[i - 1, q] * lambda.Last() ;
}
}
covariance_ = diffusion_ * Matrix.transpose(diffusion_);
}