public double discountBondOption(Option.Type type,
double strike, double maturity,
double bondMaturity)
{
List <double> accrualStartTimes
= process_.accrualStartTimes();
List <double> accrualEndTimes
= process_.accrualEndTimes();
Utils.QL_REQUIRE(accrualStartTimes.First() <= maturity && accrualStartTimes.Last() >= maturity, () =>
"capet maturity does not fit to the process");
int i = accrualStartTimes.BinarySearch(maturity);
if (i < 0)
{
// The lower_bound() algorithm finds the first position in a sequence that value can occupy
// without violating the sequence's ordering
// if BinarySearch does not find value the value, the index of the prev minor item is returned
i = ~i + 1;
}
// impose limits. we need the one before last at max or the first at min
i = Math.Max(Math.Min(i, accrualStartTimes.Count - 1), 0);
Utils.QL_REQUIRE(i < process_.size() &&
Math.Abs(maturity - accrualStartTimes[i]) < 100 * Const.QL_EPSILON &&
Math.Abs(bondMaturity - accrualEndTimes[i]) < 100 * Const.QL_EPSILON, () =>
"irregular fixings are not (yet) supported");
double tenor = accrualEndTimes[i] - accrualStartTimes[i];
double forward = process_.initialValues()[i];
double capRate = (1.0 / strike - 1.0) / tenor;
double var = covarProxy_.integratedCovariance(i, i, process_.fixingTimes()[i]);
double dis = process_.index().forwardingTermStructure().link.discount(bondMaturity);
double black = Utils.blackFormula(
(type == Option.Type.Put ? Option.Type.Call : Option.Type.Put),
capRate, forward, Math.Sqrt(var));
double npv = dis * tenor * black;
return(npv / (1.0 + capRate * tenor));
}
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())
{
Utils.QL_REQUIRE(factors_ == 1, () => "correlation matrix must be given for multi factor models");
}
else
{
Utils.QL_REQUIRE(correlation.rows() == size_ - 1 &&
correlation.rows() == correlation.columns(), () => "wrong dimesion of the correlation matrix");
Utils.QL_REQUIRE(factors_ <= size_ - 1, () => "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]);
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_);
}
