public virtual double value(double t)
{
Matrix m = param_.diffusion(t, new Vector());
double u = 0;
m.row(i_).ForEach((ii, vv) => u += vv * m.row(j_)[ii]);
return(u);
}
public override Vector evolve(double t0, Vector x0, double dt, Vector dw)
{
/* predictor-corrector step to reduce discretization errors.
*
* Short - but slow - solution would be
*
* Array rnd_0 = stdDeviation(t0, x0, dt)*dw;
* Array drift_0 = discretization_->drift(*this, t0, x0, dt);
*
* return apply(x0, ( drift_0 + discretization_
* ->drift(*this,t0,apply(x0, drift_0 + rnd_0),dt) )*0.5 + rnd_0);
*
* The following implementation does the same but is faster.
*/
int m = nextIndexReset(t0);
double sdt = Math.Sqrt(dt);
Vector f = new Vector(x0);
Matrix diff = lfmParam_.diffusion(t0, x0);
Matrix covariance = lfmParam_.covariance(t0, x0);
for (int k = m; k < size_; ++k)
{
double y = accrualPeriod_[k] * x0[k];
m1[k] = y / (1 + y);
double d = 0;
m1.GetRange(m, k + 1 - m).ForEach(
(ii, vv) => d += vv *
covariance.column(k).GetRange(m, covariance.rows() - m)[ii]);
d = (d - 0.5 * covariance[k, k]) * dt;
double r = 0;
diff.row(k).ForEach((kk, vv) => r += vv * dw[kk]);
r *= sdt;
double x = y * Math.Exp(d + r);
m2[k] = x / (1 + x);
double inner_product = 0;
m2.GetRange(m, k + 1 - m).ForEach(
(ii, vv) => inner_product += vv *
covariance.column(k).GetRange(m, covariance.rows() - m)[ii]);
f[k] = x0[k] * Math.Exp(0.5 * (d + (inner_product - 0.5 * covariance[k, k]) * dt) + r);
}
return(f);
}
public override Vector evolve(double t0, Vector x0, double dt, Vector dw)
{
// predictor-corrector step to reduce discretization errors.
int m = nextIndexReset(t0);
double sdt = Math.Sqrt(dt);
Vector f = new Vector(x0);
Matrix diff = lfmParam_.diffusion(t0, x0);
Matrix covariance = lfmParam_.covariance(t0, x0);
for (int k = m; k < size_; ++k)
{
double y = accrualPeriod_[k] * x0[k];
m1[k] = y / (1 + y);
double d = 0;
m1.GetRange(m, k + 1 - m).ForEach(
(ii, vv) => d += vv *
covariance.column(k).GetRange(m, covariance.rows() - m)[ii]);
d = (d - 0.5 * covariance[k, k]) * dt;
double r = 0;
diff.row(k).ForEach((kk, vv) => r += vv * dw[kk]);
r *= sdt;
double x = y * Math.Exp(d + r);
m2[k] = x / (1 + x);
double inner_product = 0;
m2.GetRange(m, k + 1 - m).ForEach(
(ii, vv) => inner_product += vv *
covariance.column(k).GetRange(m, covariance.rows() - m)[ii]);
f[k] = x0[k] * Math.Exp(0.5 * (d + (inner_product - 0.5 * covariance[k, k]) * dt) + r);
}
return(f);
}
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_);
}
