public static double NormalVol(double forward, double strike, double time, SABRParams sabr_params)
{
if (!sabr_params.isValid)
{
return(Double.NaN);
}
double alpha = sabr_params.Alpha;
double beta = sabr_params.Beta;
double rho = sabr_params.Rho;
double nu = sabr_params.Nu;
double K = strike;
double F = forward;
double t = time;
double A = Pow(F * K, 1.0 - beta);
double sqrtA = Sqrt(A);
double log_r;
if (Abs(F - K) > 1e-12)
{
log_r = Log(F / K);
}
else
{
double epsilon = (F - K) / K;
log_r = epsilon - 0.5 * epsilon * epsilon;
}
double z = (nu / alpha) * sqrtA * log_r;
double B = 1.0 - 2.0 * rho * z + z * z;
double C = (1.0 - beta) * (1.0 - beta) * log_r * log_r;
double D = log_r * log_r;
double tmp = (Sqrt(B) + z - rho) / (1.0 - rho);
double xx = Log(tmp);
double E_1 = (1.0 + D / 24.0 + D * D / 1920.0);
double E_2 = (1.0 + C / 24.0 + C * C / 1920.0);
double E = E_1 / E_2;
double d = 1.0 + t * (-beta * (2 - beta) * alpha * alpha / (24.0 * A) +
0.25 * rho * beta * nu * alpha / sqrtA +
(2.0 - 3.0 * rho * rho) * (nu * nu / 24.0));
double coef;
if (Abs(z * z) > 2.22045e-15)
{
coef = z / xx;
}
else
{
coef = 1.0 - 0.5 * rho * z - (3.0 * rho * rho - 2.0) * z * z / 12.0;
}
return(alpha * Pow(F * K, beta / 2.0) * E * coef * d);
}
public static double Price(double forward, double strike, double time, double rate, SABRParams sabr_params, bool isCall, bool useNormalApprox = false)
{
double price = Double.NaN;
if (sabr_params.isValid)
{
if (useNormalApprox)
{
double normal_vol = HaganSABR.NormalVol(forward, strike, time, sabr_params);
price = Bachelier.Price(forward, strike, time, rate, normal_vol, isCall);
}
else
{
double black_vol = HaganSABR.BlackVol(forward, strike, time, sabr_params);
price = Black.Price(forward, strike, time, rate, black_vol, isCall);
}
}
return(price);
}
