private double GetSecondDerivativeToStrike(double t, double k)
{
// there is possibility that the bump sizes are different between forward and backward.
// we use the minimum of them to calculate the second order derivative.
double bumpsize = PriceBump.MinBump(k);
return((ImpliedVol.GetValue(t, k + bumpsize) + ImpliedVol.GetValue(t, k - bumpsize) - 2 * ImpliedVol.GetValue(t, k)) /
(bumpsize * bumpsize));
}
