public static double ibachelier(OptionType optType, double F, double K, double T, double premium, bool safe = false)
{
if (T <= 0.0)
{
throw FS.FailWith($"T must be postive, got {T}");
}
var epsilon = optType.ToEpsilon();
var intrinsic = Math.Max(epsilon * (F - K), 0.0);
if (premium <= intrinsic)
{
if (DoubleUtils.ApproximatelyEqual(premium, intrinsic, DoubleUtils.DoubleEpsilon))
{
return(0.0);
}
if (safe)
{
return(0.0);
}
throw FS.FailWith($"premium must be larger than intrinsic. Got premium = {premium}, vs intrinsic = {intrinsic}"); //!
}
if (F == K)
{
return(premium * Math.Sqrt(2.0 * Math.PI / T));
}
var sqrtT = Math.Sqrt(T);
var phiStar = -Math.Abs((premium - intrinsic) / (K - F));
var xBar = 0.0;
if (phiStar < -0.001882039271)
{
var g = 1.0 / (phiStar - 0.5);
var g2 = g * g;
var zeta = (0.032114372355 - g2 * (0.016969777977 - g2 * (2.6207332461e-3 - 9.6066952861e-5 * g2)))
/ (1.0 - g2 * (0.6635646938 - g2 * (0.14528712196 - 0.010472855461 * g2)));
xBar = g * (1.0 / Math.Sqrt(2.0 * Math.PI) + zeta * g2);
}
else
{
var h = Math.Sqrt(-Math.Log(-phiStar));
xBar = (9.4883409779 - h * (9.6320903635 - h * (0.58556997323 + 2.1464093351 * h)))
/ (1 - h * (0.65174820867 + h * (1.5120247828 + 6.6437847132e-5 * h)));
}
var xBar2 = xBar * xBar;
var nxBar = SpecialFunction.pdf_normal(xBar);
var phiTildaXBar = SpecialFunction.cdf_normal(xBar) + nxBar / xBar;
var q = (phiTildaXBar - phiStar) / nxBar;
var xStar = xBar + (3.0 * q * xBar2 * (2.0 - q * xBar * (2.0 + xBar2)))
/ (6.0 + q * xBar * (-12.0 + xBar * (6.0 * q + xBar * (-6.0 + q * xBar * (3.0 + xBar2)))));
return(Math.Abs((K - F) / (xStar * sqrtT)));
}
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 black76(OptionType optType, double F, double K, double sdev)
{
var num = optType.ToEpsilon();
if (sdev < 0.0)
{
throw FS.FailWith($"sdev must be positive. Got {sdev}");
}
if (sdev == 0.0 || K <= 0.0)
{
return(Math.Max(num * (F - K), 0.0));
}
else
{
var num2 = (Math.Log(F / K) + 0.5 * sdev * sdev) / sdev;
var num3 = num2 - sdev;
return(num * (F * SpecialFunction.cdf_normal(num * num2) -
K * SpecialFunction.cdf_normal(num * num3)));
}
}
public static double beta_black_b(double beta, OptionType optType, double F, double K, double T, double sigma
, ref double beta_b, ref double F_b, ref double K_b, ref double T_b, ref double sigma_b, double res_b)
{
if (T < 0.0)
{
throw FS.FailWith($"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);
}
}
