// Calculate the Gauthier coefficients
public double[] GauthierCoefficients(double kappa, double theta, double v0, double S, double K, double T, double rf, double q)
{
BlackScholesPrice BS = new BlackScholesPrice();
double x = Math.Log(S);
double kT = kappa * T;
double m0 = Math.Exp(-kT) * (Math.Exp(kT) - 1) / kappa;
double m1 = T - m0;
double varT = m0 * v0 + m1 * theta;
double p0 = Math.Exp(-kT) * (Math.Exp(kT) - kT - 1) / kappa / kappa;
double p1 = Math.Exp(-kT) * (Math.Exp(kT) * (kT - 2) + kT + 2) / kappa / kappa;
double q0 = Math.Exp(-kT) * (2 * Math.Exp(kT) - kT * (kT + 2) - 2) / 2 / kappa / kappa / kappa;
double q1 = Math.Exp(-kT) * (2 * Math.Exp(kT) * (kT - 3) + kT * (kT + 4) + 6) / 2 / kappa / kappa / kappa;
double r0 = Math.Exp(-2 * kT) * (2 * Math.Exp(2 * kT) - 4 * Math.Exp(kT) * kT - 2) / 4 / kappa / kappa / kappa;
double r1 = Math.Exp(-2 * kT) * (Math.Exp(2 * kT) * (2 * kT - 5) + 4 * Math.Exp(kT) * (kT + 1) + 1) / 4 / kappa / kappa / kappa;
double[] BSderiv = BS.BlackScholesDerivatives(kappa, theta, v0, S, K, T, rf, q);
double P11 = BSderiv[0];
double P21 = BSderiv[1];
double P02 = BSderiv[2];
double P22 = BSderiv[3];
double y = varT;
// Black Scholes Put Price
double g = Math.Pow(y, -0.5) * (-x + Math.Log(K) - (rf - q) * T) - 0.5 * Math.Sqrt(y);
double f = Math.Pow(y, -0.5) * (-x + Math.Log(K) - (rf - q) * T) + 0.5 * Math.Sqrt(y);
double BSPut = K * Math.Exp(-rf * T) * BS.NormCDF(f) - S * Math.Exp(-q * T) * BS.NormCDF(g);
double A = BSPut;
double B = (v0 * r0 + theta * r1) * P02;
double C = (v0 * p0 + theta * p1) * P11;
double D = (v0 * q0 + theta * q1) * P21 + 0.5 * Math.Pow(v0 * p0 + theta * p1, 2) * P22;
double[] output = new double[4];
output[0] = A;
output[1] = B;
output[2] = C;
output[3] = D;
return(output);
}
// public double Algorithm for Black Scholes Implied Volatility =================================================================================
public double BisecBSIV(string PutCall, double S, double K, double rf, double q, double T, double a, double b, double MktPrice, double Tol, int MaxIter)
{
BlackScholesPrice BS = new BlackScholesPrice();
double lowCdif = MktPrice - BS.BlackScholes(S, K, T, rf, q, a, PutCall);
double highCdif = MktPrice - BS.BlackScholes(S, K, T, rf, q, b, PutCall);
double BSIV = 0.0;
double midP;
if (lowCdif * highCdif > 0.0)
{
BSIV = -1.0;
}
else
{
for (int x = 0; x <= MaxIter; x++)
{
midP = (a + b) / 2.0;
double midCdif = MktPrice - BS.BlackScholes(S, K, T, rf, q, midP, PutCall);
if (Math.Abs(midCdif) < Tol)
{
break;
}
else
{
if (midCdif > 0.0)
{
a = midP;
}
else
{
b = midP;
}
}
BSIV = midP;
}
}
return(BSIV);
}
