public static double beta_black(double beta, OptionType optType, double F, double K, double T, double sigma)
{
if (T < 0.0)
{
throw FS.FailWith($"T < 0 not allowed, {T}");
}
if (sigma < 0.0)
{
throw FS.FailWith($"sigma < 0 not allowed {sigma}");
}
var stdev = sigma * Math.Sqrt(T);
if (stdev == 0.0)
{
return(Math.Max(optType.ToEpsilon() * (F - K), 0.0));
}
var mu = inv_m1_beta_black(beta, F, stdev);
var d = (inv_g(beta, K) - mu) / stdev;
var t1 = K * SpecialFunction.cdf_normal(d);
var t2 = beta_black_trunc(beta, mu, stdev, d);
var put = t1 - t2;
var intrinsic = Math.Max(optType.ToEpsilon() * (F - K), 0.0);
if (optType == OptionType.Put)
{
return(Math.Max(put, intrinsic));
}
else if (optType == OptionType.Call)
{
return(Math.Max(put + F - K, intrinsic));
}
else
{
throw FS.E_CASE(optType);
}
}
public static double beta_black_b(double beta, OptionType optType, double F, double K, double T, double sigma
, ref double beta_b, ref double F_b, ref double K_b, ref double T_b, ref double sigma_b, double res_b)
{
if (T < 0.0)
{
throw FS.FailWith($"T < 0 not allowed, {T}");
}
if (sigma < 0.0)
{
throw FS.FailWith($"sigma < 0 not allowed {sigma}");
}
var sqrtT = Math.Sqrt(T);
var stdev = sigma * sqrtT;
if (stdev == 0.0)
{
return(Math.Max(optType.ToEpsilon() * (F - K), 0.0));
}
var dmu_dbeta = 0.0;
var dmu_dF = 0.0;
var dmu_dstdev = 0.0;
var mu = inv_m1_beta_black_b(beta, F, stdev, ref dmu_dbeta, ref dmu_dF, ref dmu_dstdev, 1.0);
var digb_dbeta = 0.0;
var digb_dK = 0.0;
var igb = inv_g_b(beta, K, ref digb_dbeta, ref digb_dK, 1.0);
var d = (igb - mu) / stdev;
var dNd_dd = 0.0;
var Nd = SpecialFunction.cdf_normal_b(d, ref dNd_dd, 1.0);
var t1 = K * Nd;
var dt2_dbeta = 0.0;
var dt2_dmu = 0.0;
var dt2_dstdev = 0.0;
var dt2_dd = 0.0;
var t2 = beta_black_trunc_b(beta, mu, stdev, d, ref dt2_dbeta, ref dt2_dmu, ref dt2_dstdev, ref dt2_dd, 1.0);
var res = t1 - t2;
// now rewind
var t1_b = res_b;
var t2_b = -res_b;
beta_b += t2_b * dt2_dbeta;
var mu_b = t2_b * dt2_dmu;
var stdev_b = t2_b * dt2_dstdev;
var d_b = t2_b * dt2_dd;
K_b += t1_b * Nd;
var Nd_b = t1_b * K;
d_b += Nd_b * dNd_dd;
var igb_b = d_b / stdev;
mu_b += -d_b / stdev;
stdev_b += -d_b * (igb - mu) / stdev / stdev;
beta_b += igb_b * digb_dbeta;
K_b += igb_b * digb_dK;
beta_b += mu_b * dmu_dbeta;
F_b += mu_b * dmu_dF;
stdev_b += mu_b * dmu_dstdev;
sigma_b += stdev_b * sqrtT;
T_b += stdev_b * sigma / (2.0 * sqrtT);
if (optType == OptionType.Put)
{
return(res);
}
else if (optType == OptionType.Call)
{
F_b += res_b;
K_b += -res_b;
return(res + F - K);
}
else
{
throw FS.E_CASE(optType);
}
}
