public static double BachelierCallPrice(double spot, double lambda, double mat, double strike)
{
double d = (spot - strike) / (lambda * Math.Sqrt(mat));
double NormalPdf = 1.0; // calculate this
return(MyMath.NormalCdf(d) * (spot - strike) + lambda * Math.Sqrt(mat) * NormalPdf);
}
public static void BlackScholesNoReset(ADouble vol, ADouble spot, ADouble rate, ADouble time, ADouble mat, ADouble strike)
{
ADouble Help1 = vol * ADouble.Sqrt(mat - time);
ADouble d1 = 1.0 / Help1 * (ADouble.Log(spot / strike) + (rate + 0.5 * ADouble.Pow(vol, 2)) * (mat - time));
ADouble d2 = d1 - vol * ADouble.Sqrt(mat - time);
ADouble Out = MyMath.NormalCdf(d1) * spot - strike * ADouble.Exp(-rate * (mat - time)) * MyMath.NormalCdf(d2);
}
public static double BsCallPrice(double spot, double vol, double mat, double strike, double rate)
{
double std = Math.Sqrt(mat) * vol;
double halfVar = (rate + vol * vol * 0.5) * mat;
double d1 = (Math.Log(spot / strike) + halfVar) / std;
double d2 = d1 - std;
return(spot * MyMath.NormalCdf(d1) - strike * MyMath.NormalCdf(d2) * Math.Exp(-rate * mat));
}
public static void BlackScholes(ADouble vol, ADouble spot, ADouble rate, ADouble time, ADouble mat, ADouble strike)
{
AADTape.ResetTape();
AADTape.Initialize(new ADouble[] { vol, spot, rate, time, mat, strike });
ADouble Help1 = vol * ADouble.Sqrt(mat - time);
ADouble d1 = 1.0 / Help1 * (ADouble.Log(spot / strike) + (rate + 0.5 * ADouble.Pow(vol, 2)) * (mat - time));
ADouble d2 = d1 - vol * ADouble.Sqrt(mat - time);
ADouble Out = MyMath.NormalCdf(d1) * spot - strike * ADouble.Exp(-rate * (mat - time)) * MyMath.NormalCdf(d2);
Console.WriteLine("");
Console.WriteLine("BLACK-SCHOLES TEST. Value: " + Out.Value);
AADTape.InterpretTape();
AADTape.PrintTape();
AADTape.ResetTape();
}