public static double ComputeQuantile(double forward, double maturity, Func <double, double> vol, double proba)
{
double s = vol(forward) * Math.Sqrt(maturity);
double kGuess = forward * Math.Exp(s * (NormalDistribution.FastCumulativeInverse(proba) + 0.5 * s));
Func <double, double> cumErr = m => Cumulative(forward, maturity, vol, forward * Math.Exp(m)) - proba;
double m1, m2;
RootUtils.Bracket(cumErr, Math.Log(kGuess / forward), 0.0, out m1, out m2);
var mQuantile = RootUtils.Brenth(cumErr, m1, m2, forward * 1.0e-5, DoubleUtils.MachineEpsilon);
return(forward * Math.Exp(mQuantile));
}
public void FastVsPreciseInverse()
{
var bound = NormalDistribution.CumulativeInverse(1.0e-6);
var grid = GridUtils.RegularGrid(bound, -bound, 1000);
foreach (var x in grid)
{
var p = NormalDistribution.Cumulative(x);
var precise = NormalDistribution.CumulativeInverse(p);
var fast = NormalDistribution.FastCumulativeInverse(p);
var errRelative = Math.Abs(fast - precise);
Assert.IsTrue(errRelative < 3.0e-9);
}
}
