public static void test_beta_black_perf()
{
Console.WriteLine("Computing ... ");
var N = 100000;
var tic = DateTime.Now;
for (var i = 0; i < N; ++i)
{
ClosedForm.black76(OptionType.Put, 10.0, 4.0, 0.5, 0.4);
ClosedForm.black76(OptionType.Put, 10.0, 8.0, 1.5, 0.4);
ClosedForm.black76(OptionType.Put, 10.0, 4.0, 0.5, 0.4);
ClosedForm.black76(OptionType.Put, 10.0, 8.0, 1.5, 0.4);
ClosedForm.black76(OptionType.Put, 10.0, 4.0, 0.5, 0.4);
ClosedForm.black76(OptionType.Put, 10.0, 8.0, 1.5, 0.4);
}
var toc = DateTime.Now;
var ticBB = DateTime.Now;
for (var i = 0; i < N; ++i)
{
BetaBlack.beta_black(0.1, OptionType.Put, 10.0, 4.0, 0.5, 0.4);
BetaBlack.beta_black(0.1, OptionType.Put, 8.0, 4.0, 0.5, 0.4);
BetaBlack.beta_black(0.5, OptionType.Put, 10.0, 4.0, 0.5, 0.4);
BetaBlack.beta_black(0.5, OptionType.Put, 8.0, 4.0, 0.5, 0.4);
BetaBlack.beta_black(0.5, OptionType.Put, -10.0, -14.0, 0.5, 0.4);
BetaBlack.beta_black(0.5, OptionType.Put, -8.0, -10.0, 0.5, 0.4);
}
var tocBB = DateTime.Now;
var ticBBP = DateTime.Now;
var ignore = 0.0;
for (var i = 0; i < N; ++i)
{
BetaBlack.beta_black_b(0.1, OptionType.Put, 10.0, 4.0, 0.5, 0.4, ref ignore, ref ignore, ref ignore,
ref ignore, ref ignore, 1.0);
BetaBlack.beta_black_b(0.1, OptionType.Put, 8.0, 4.0, 0.5, 0.4, ref ignore, ref ignore, ref ignore,
ref ignore, ref ignore, 1.0);
BetaBlack.beta_black_b(0.5, OptionType.Put, 10.0, 4.0, 0.5, 0.4, ref ignore, ref ignore, ref ignore,
ref ignore, ref ignore, 1.0);
BetaBlack.beta_black_b(0.5, OptionType.Put, 8.0, 4.0, 0.5, 0.4, ref ignore, ref ignore, ref ignore,
ref ignore, ref ignore, 1.0);
BetaBlack.beta_black_b(0.5, OptionType.Put, -10.0, -14.0, 0.5, 0.4, ref ignore, ref ignore, ref ignore,
ref ignore, ref ignore, 1.0);
BetaBlack.beta_black_b(0.5, OptionType.Put, -8.0, -10.0, 0.5, 0.4, ref ignore, ref ignore, ref ignore,
ref ignore, ref ignore, 1.0);
}
var tocBBP = DateTime.Now;
Console.WriteLine("Done");
Console.WriteLine($"Black: {(toc - tic).TotalMilliseconds}");
Console.WriteLine($"B-Black: {(tocBB - ticBB).TotalMilliseconds}");
Console.WriteLine($"First Order Risk B-Black : {(tocBBP - ticBBP).TotalMilliseconds}");
Console.WriteLine($"PV time in # blacks: {(tocBB - ticBB).TotalMilliseconds / (toc - tic).TotalMilliseconds}");
Console.WriteLine($"Risk first order time in # blacks: {(tocBBP - ticBBP).TotalMilliseconds / (toc - tic).TotalMilliseconds}");
}
public BetaBlackPack(double beta, OptionType callPut, double f, double k, double t, double sigma)
{
if (beta < 0 || beta >= 1.0)
{
throw FS.FailWith($"Beta must be in [0, 1.0), got {beta}");
}
if (sigma <= 0.0)
{
throw FS.FailWith($"Sigma must be positive, got {sigma}");
}
Beta = beta;
CallPut = callPut;
F = f;
K = k;
T = t;
Sigma = sigma;
//! Nota bene: Use AD for first order derivatives and FD on AD for second order
//
// Mu = BetaBlack.inv_m1_beta_black(beta, f, sigma * Math.Sqrt(t));
double beta_b = 0.0;
double f_b = 0.0;
double k_b = 0.0;
double t_b = 0.0;
double sigma_b = 0.0;
Price = BetaBlack.beta_black_b(beta, callPut, f, k, t, sigma, ref beta_b, ref f_b, ref k_b, ref t_b, ref sigma_b, 1.0);
dPV_dS = f_b;
dPV_dK = k_b;
dPV_dT = t_b;
dPV_dVol = sigma_b;
dPV_dBeta = beta_b;
var eps = Math.Sqrt(DoubleUtils.DoubleEpsilon);
{
var dF = eps * (1.0 + Math.Abs(f));
double betaUp_b = 0.0;
double fUp_b = 0.0;
double kUp_b = 0.0;
double tUp_b = 0.0;
double sigmaUp_b = 0.0;
double pUp = BetaBlack.beta_black_b(beta, callPut, f + dF, k, t, sigma, ref betaUp_b, ref fUp_b, ref kUp_b, ref tUp_b, ref sigmaUp_b, 1.0);
double betaDown_b = 0.0;
double fDown_b = 0.0;
double kDown_b = 0.0;
double tDown_b = 0.0;
double sigmaDown_b = 0.0;
double pDown = BetaBlack.beta_black_b(beta, callPut, f - dF, k, t, sigma, ref betaDown_b, ref fDown_b, ref kDown_b, ref tDown_b, ref sigmaDown_b, 1.0);
d2PV_dFdBeta = (betaUp_b - betaDown_b) / (2.0 * dF);
d2PV_dS2 = (fUp_b - fDown_b) / (2.0 * dF);
d2PV_dKdS = (kUp_b - kDown_b) / (2.0 * dF);
d2PV_dSdT = (tUp_b - tDown_b) / (2.0 * dF);
d2PV_dSdVol = (sigmaUp_b - sigmaDown_b) / (2.0 * dF);
}
{
var dK = eps * (1.0 + Math.Abs(k));
double betaUp_b = 0.0;
double fUp_b = 0.0;
double kUp_b = 0.0;
double tUp_b = 0.0;
double sigmaUp_b = 0.0;
double pUp = BetaBlack.beta_black_b(beta, callPut, f, k + dK, t, sigma, ref betaUp_b, ref fUp_b, ref kUp_b, ref tUp_b, ref sigmaUp_b, 1.0);
double betaDown_b = 0.0;
double fDown_b = 0.0;
double kDown_b = 0.0;
double tDown_b = 0.0;
double sigmaDown_b = 0.0;
double pDown = BetaBlack.beta_black_b(beta, callPut, f, k - dK, t, sigma, ref betaDown_b, ref fDown_b, ref kDown_b, ref tDown_b, ref sigmaDown_b, 1.0);
d2PV_dKdBeta = (betaUp_b - betaDown_b) / (2.0 * dK);
// d2PV_dKdS = (fUp_b - fDown_b) / (2.0 * dK);
d2PV_dK2 = (kUp_b - kDown_b) / (2.0 * dK);
d2PV_dKdT = (tUp_b - tDown_b) / (2.0 * dK);
d2PV_dVoldK = (sigmaUp_b - sigmaDown_b) / (2.0 * dK);
}
{
var dSigma = eps * (1.0 + Math.Abs(sigma));
double betaUp_b = 0.0;
double fUp_b = 0.0;
double kUp_b = 0.0;
double tUp_b = 0.0;
double sigmaUp_b = 0.0;
double pUp = BetaBlack.beta_black_b(beta, callPut, f, k, t, sigma + dSigma, ref betaUp_b, ref fUp_b, ref kUp_b, ref tUp_b, ref sigmaUp_b, 1.0);
double betaDown_b = 0.0;
double fDown_b = 0.0;
double kDown_b = 0.0;
double tDown_b = 0.0;
double sigmaDown_b = 0.0;
double pDown = BetaBlack.beta_black_b(beta, callPut, f, k, t, sigma - dSigma, ref betaDown_b, ref fDown_b, ref kDown_b, ref tDown_b, ref sigmaDown_b, 1.0);
d2PV_dVoldBeta = (betaUp_b - betaDown_b) / (2.0 * dSigma);
// d2PV_dSdVol = (fUp_b - fDown_b) / (2.0 * dSigma);
// d2PV_dVoldK = (kUp_b - kDown_b) / (2.0 * dSigma);
d2PV_dVoldT = (tUp_b - tDown_b) / (2.0 * dSigma);
d2PV_dVol2 = (sigmaUp_b - sigmaDown_b) / (2.0 * dSigma);
}
}
