public double CashBpvAverage(double start, double end)
{
if (end > start)
{
return((cashBpvIntegral.Eval(end) - cashBpvIntegral.Eval(start)) / (end - start));
}
return(cashBpvIntegral.Eval(start));
}
public override RnRFunction Zc(DateTime date, DateTime maturity, double fwdZc)
{
Contract.Requires(date <= maturity);
double d = time[date];
var drift = driftTerm.Eval(d);
return(HwModelUtils.ZcFunction(time[maturity] - d, fwdZc, new[] { meanReversion }, new[, ] {
{ drift }
}));
}
private static Func <double, double> StepLocalVol(DateTime startDate, DateTime endDate, LocalVolatilityModel model)
{
var time = model.Time;
double start = time[startDate];
double end = time[endDate];
VolatilitySurface volSurface = model.VolSurface;
RrFunction stepLocalVariance = volSurface.LocalVariance.TimeAveragedSlice(start, end);
var moneyness = model.Moneyness.Moneyness(start);
Func <double, double> localVol = logSpot => Math.Sqrt(stepLocalVariance.Eval(moneyness(Math.Exp(logSpot))));
var gridLocalVol = LocalVolDiscretization(localVol, volSurface, 0.5 * (start + end));
return(gridLocalVol.Eval);
}
public double Eval(double t, double y)
{
var stepIndex = maturityStepSearcher.LocateLeftIndex(t);
double v, dVdY, d2Vd2Y, dVdT;
if (stepIndex < 0)
{
double w = t / maturities[0];
if (Math.Abs(w) < 1.0e-10)
{
return(shortLocalVar.Eval(y));
}
v = w * vs[0].Eval(y);
dVdY = w * dVdYs[0].Eval(y);
d2Vd2Y = w * d2Vd2Ys[0].Eval(y);
dVdT = vs[0].Eval(y) / maturities[0];
}
else if (stepIndex == maturities.Length - 1)
{
double w = t / maturities[maturities.Length - 1];
v = vs[stepIndex].Eval(y) * w;
dVdY = dVdYs[stepIndex].Eval(y) * w;
d2Vd2Y = d2Vd2Ys[stepIndex].Eval(y) * w;
dVdT = dVdTs[stepIndex].Eval(y);
}
else
{
double w = (t - maturities[stepIndex]) / (maturities[stepIndex + 1] - maturities[stepIndex]);
v = (1.0 - w) * vs[stepIndex].Eval(y) + w * vs[stepIndex + 1].Eval(y);
dVdY = (1.0 - w) * dVdYs[stepIndex].Eval(y) + w * dVdYs[stepIndex + 1].Eval(y);
d2Vd2Y = (1.0 - w) * d2Vd2Ys[stepIndex].Eval(y) + w * d2Vd2Ys[stepIndex + 1].Eval(y);
dVdT = dVdTs[stepIndex].Eval(y);
}
// dv/dt
// local variance = ------------------------------------------------------------------------------------
// (y * (dv/dy) / (2 * v) - 1)^2 + 1/2 * (d^2 v/dy^2) - 1/4 * (1/4 + 1/v) * (dv/dy)^2
double localVar = 0.5 * y * dVdY / v - 1.0;
localVar = localVar * localVar + 0.5 * d2Vd2Y - 0.25 * (0.25 + 1.0 / v) * dVdY * dVdY;
localVar = dVdT / localVar;
return(localVar);
}
public override double Zc(double d)
{
return Math.Exp(-zcRate.Eval(d) * d);
}