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 ADouble InvNormalCdf(ADouble p)
{
// Courtesy to Antoine Savine (Danske Bank)
if (p > 0.5)
{
return(-InvNormalCdf(1.0 - p));
}
ADouble Up = new ADouble();
if (p < 1.0e-15)
{
Up = new ADouble(1.0e-15);
}
else
{
Up = p;
}
// constants
double a0 = 2.50662823884;
double a1 = -18.61500062529;
double a2 = 41.39119773534;
double a3 = -25.44106049637;
double b0 = -8.47351093090;
double b1 = 23.08336743743;
double b2 = -21.06224101826;
double b3 = 3.13082909833;
double c0 = 0.3374754822726147;
double c1 = 0.9761690190917186;
double c2 = 0.1607979714918209;
double c3 = 0.0276438810333863;
double c4 = 0.0038405729373609;
double c5 = 0.0003951896511919;
double c6 = 0.0000321767881768;
double c7 = 0.0000002888167364;
double c8 = 0.0000003960315187;
ADouble x = Up - 0.5;
ADouble r = new ADouble();
if (Math.Abs(x.Value) < 0.42)
{
r = x * x;
r = x * (((a3 * r + a2) * r + a1) * r + a0) / ((((b3 * r + b2) * r + b1) * r + b0) * r + 1.0);
return(r);
}
// Log-Log approximation
r = Up;
r = ADouble.Log(-ADouble.Log(r));
r = c0 + r * (c1 + r * (c2 + r * (c3 + r * (c4 + r * (c5 + r * (c6 + r * (c7 + r * c8)))))));
r = -r;
return(r);
}
public static void FuncLog(ADouble x)
{
AADTape.ResetTape();
AADTape.Initialize(new ADouble[] { x });
// Derivative: Fx(x) = 3 + 3/x
ADouble Temp = 3.0 * x + 3.0 * ADouble.Log(x * 4.0) + 50.0;
AADTape.InterpretTape();
AADTape.PrintTape();
AADTape.ResetTape();
}
public static void FuncPow(ADouble x, double k)
{
AADTape.ResetTape();
AADTape.Initialize(new ADouble[] { x });
ADouble Out = 3.0 * ADouble.Log(x) + 5.0 * ADouble.Pow(x, k);
Console.WriteLine(" ");
Console.WriteLine("Testing Adjoint differentiation of a function involving powers");
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();
}
// For example in thesis
public static ADouble ExampleFunctionThesis(ADouble x1, ADouble x2)
{
return(2.0 * x1 * x2 + ADouble.Log(x1 - 4.0 * x2));
}