public static double[][] ComputeLocalVarianceOnGridFromCalls(this IVolSurface VanillaSurface, double[][] strikes, double[] timeSteps, Func <double, double> forwardFunc)
{
var numberOfTimesteps = timeSteps.Length;
var deltaK = 0.001 * forwardFunc(timeSteps[0]);
var lvGrid = new double[numberOfTimesteps - 1][];
var fwds = timeSteps.Select(t => forwardFunc(t)).ToArray();
//ParallelUtils.Instance.For(1, numberOfTimesteps, 1, it =>
for (var it = 1; it < numberOfTimesteps; it++)
{
var T = timeSteps[it];
var T1 = timeSteps[it - 1];
var fwd = fwds[it];
var fwdtm1 = fwds[it - 1];
var rmq = Log(fwd / fwdtm1) / (T - T1);
var numberOfStrikes = strikes[it - 1].Length;
var cInterp = VanillaSurface.GeneratePremiumInterpolator(numberOfStrikes * 2, T, fwd, OptionType.C);
lvGrid[it - 1] = new double[numberOfStrikes];
if (numberOfStrikes > 1)
{
for (var ik = 0; ik < numberOfStrikes; ik++)
{
var K = strikes[it][ik];
var V = VanillaSurface.GetVolForAbsoluteStrike(K, T, fwd);
var C = BlackFunctions.BlackPV(fwd, K, 0.0, T, V, OptionType.C);
var Vtm1 = VanillaSurface.GetVolForAbsoluteStrike(K, T1, fwdtm1);
//var dcdt = -BlackFunctions.BlackTheta(fwd, K, 0.0, T, V, OptionType.C);
var dcdt = -(BlackFunctions.BlackPV(fwdtm1, K, 0.0, T1, Vtm1, OptionType.C) - C) / (T - T1);
var dcdk = cInterp.FirstDerivative(K);
var d2cdk2 = cInterp.SecondDerivative(K);
var localVariance = d2cdk2 == 0 ? V * V : (dcdt - rmq * (C - K * dcdk)) / (0.5 * K * K * d2cdk2);
lvGrid[it - 1][ik] = localVariance;
}
}
else
{
var K = strikes[it][0];
var V = VanillaSurface.GetVolForAbsoluteStrike(K, T, fwd);
lvGrid[it - 1][0] = V * V;
}
}//, false).Wait();
return(lvGrid);
}
public static double AmericanFutureOptionPV(double forward, double strike, double riskFree, double expTime, double volatility, OptionType CP)
{
var blackPV = BlackFunctions.BlackPV(forward, strike, riskFree, expTime, volatility, CP);
if (riskFree == 0)
{
return(blackPV);
}
var n = System.Math.Max(32, (int)System.Math.Round(365.0 / 2.0 * expTime));
var PV = AmericanPV(expTime, forward, strike, riskFree, volatility, CP, riskFree, n);
return(PV.SafeMax(blackPV));
}
public static double AmericanFutureOptionPV(double forward, double strike, double RiskFree, double expTime, double Volatility, OptionType CP)
{
var n = (int)System.Math.Round(365 * expTime);
var blackPV = BlackFunctions.BlackPV(forward, strike, RiskFree, expTime, Volatility, CP);
if (RiskFree == 0) //american option under zero rates has no benefit to ever exercise early
{
return(blackPV);
}
var PV = AmericanPV(expTime, forward, strike, RiskFree, Volatility, CP, RiskFree, n);
return(PV.SafeMax(blackPV));
}