public static double inv_m1_beta_black_cxv(double beta, double f, double sigma)
{
var s2 = sigma * sigma;
var igb = inv_g(beta, f);
var fac = -0.5 * s2;
var rf = FS.fun((double cxv) =>
{
var mu = igb + fac * cxv;
var f0 = m1_beta_black(beta, mu, sigma);
return(f - f0);
});
var alpha = 0.5 * beta * s2;
var guess = alpha == 0.0 ? 1.0 : Math.Min(1.0, Math.Max(0.0, (f + alpha) / alpha));
var lo = guess - 1e-3;
var hi = guess + 1e-3;
var tGuess = rf(alpha);
if (DoubleUtils.ApproximatelyEqual(tGuess, 0.0, 100.0 * DoubleUtils.DoubleEpsilon))
{
return(igb + fac * alpha);
}
NumericalRecipes.zbrac(rf, ref lo, ref hi);
var cxvRoot = Brent.FindRoot(rf, lo, hi);
return(igb + fac * cxvRoot);
}
public static double beta_black_break_even_to_sigma(double beta, double f, double t, double breakEven, double dt = 1.0 / 365.0)
{
var rf = FS.fun((double sigma) => beta_black_break_even(beta, f, t, sigma, dt) - breakEven);
var x1 = 1.0;
var x2 = 5.0;
NumericalRecipes.zbrac(rf, ref x1, ref x2);
return(Brent.FindRoot(rf, x1, x2));
}
public static double ibeta_black(double beta, OptionType optType, double F, double K, double T, double premium)
{
var rf = FS.fun((double sigma) => beta_black(beta, optType, F, K, T, sigma) - premium);
var lo = 1.0;
var hi = 5.0; // If very deep in-out of the money, will fail. f(lo) = f(hi), zbrac only moves low
NumericalRecipes.zbrac(rf, ref lo, ref hi);
return(Brent.FindRoot(rf, lo, hi));
}
public static double inv_m1_beta_black_brent(double beta, double f, double sigma)
{
var guess = inv_m1_beta_black_convexity(beta, f, sigma);
var shift = 1.5e-8 * (Math.Max(1.0, Math.Abs(guess)));
var lo = guess - shift;
var hi = guess + shift;
var rf = FS.fun((double mu) =>
{
var rr = m1_beta_black(beta, mu, sigma);
return(rr - f);
});
return(Brent.FindRootExpand(rf, lo, hi));
}