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 void FuncExp(ADouble x)
{
AADTape.ResetTape();
AADTape.Initialize(new ADouble[] { x });
// Derivative: Fx(x) = 3 + 3*exp(3*x)
ADouble Temp = 3.0 * x + ADouble.Exp(3.0 * x) + 50.0;
AADTape.InterpretTape();
AADTape.PrintTape();
AADTape.ResetTape();
}
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();
}
public static ADouble NormalCdf(ADouble x)
{
// Courtesy of Antoine Savine (Danske Bank)
if (x < -10.0)
{
return(0.0);
}
else if (x > 10.0)
{
return(1.0);
}
if (x < 0.0)
{
return(1.0 - NormalCdf(-x));
}
// Constants
double p = 0.2316419;
double b1 = 0.319381530;
double b2 = -0.356563782;
double b3 = 1.781477937;
double b4 = -1.821255978;
double b5 = 1.330274429;
// Transform
ADouble t = 1.0 / (1.0 + p * x);
ADouble pol = t * (b1 + t * (b2 + t * (b3 + t * (b4 + t * b5))));
ADouble pdf = 0.0;
if (x < -10.0 || 10.0 < x)
{
pdf = 0.0;
}
else
{
pdf = ADouble.Exp(-0.5 * x * x) / MyMathConstants.SqrtTwoPi;
}
return(1.0 - pdf * pol);
}
public ADouble DiscFactor(DateTime asOf, DateTime date, DayCount dayCount, InterpMethod interpolation)
{
return(ADouble.Exp(-1.0 * ZeroRate(date, interpolation) * DateHandling.Cvg(asOf, date, dayCount)));
}
