/// <summary>
/// Black Scholes European Call and Put Option.
/// </summary>
/// <param name="sigma"></param>
/// <param name="t"></param>
/// <param name="k"></param>
/// <param name="q"></param>
/// <param name="s0"></param>
/// <param name="r"></param>
/// <returns></returns>
private static Vector BlackSholes(double sigma, double t, double k, double q, double s0, double r)
{
// Compute d1 in BS model.
double d1 = (Math.Log(s0 / k) + (r + 0.5 * sigma * sigma) * t) / (sigma * Math.Sqrt(t));
// Compute d2 in BS model.
double d2 = d1 - (sigma * Math.Sqrt(t));
Fairmat.Statistics.Normal nom = new Fairmat.Statistics.Normal(0, 1);
// The cumulative normal distribution functions for calls
double ncd1 = nom.Cdf(d1);
double ncd2 = nom.Cdf(d2);
// The cumulative normal distribution functions for puts
double npd1 = nom.Cdf(-d1);
double npd2 = nom.Cdf(-d2);
Vector bs_var = (Vector) new double[] { 0, 0 };
// Calculate the cbls.
bs_var[0] = s0 * ncd1 - k * Math.Exp(-r * t) * ncd2;
// Calculate the pbls.
bs_var[1] = k * Math.Exp(-r * t) * npd2 - s0 * npd1;
return(bs_var);
}
/// <summary>
/// Black Scholes European Call and Put Option.
/// </summary>
/// <param name="sigma"></param>
/// <param name="t"></param>
/// <param name="k"></param>
/// <param name="q"></param>
/// <param name="s0"></param>
/// <param name="r"></param>
/// <returns></returns>
private static Vector BlackSholes(double sigma, double t, double k, double q, double s0, double r)
{
// Compute d1 in BS model.
double d1 = (Math.Log(s0 / k) + (r + 0.5 * sigma * sigma) * t) / (sigma * Math.Sqrt(t));
// Compute d2 in BS model.
double d2 = d1 - (sigma * Math.Sqrt(t));
Fairmat.Statistics.Normal nom = new Fairmat.Statistics.Normal(0, 1);
// The cumulative normal distribution functions for calls
double ncd1 = nom.Cdf(d1);
double ncd2 = nom.Cdf(d2);
// The cumulative normal distribution functions for puts
double npd1 = nom.Cdf(-d1);
double npd2 = nom.Cdf(-d2);
Vector bs_var = (Vector)new double[] { 0, 0 };
// Calculate the cbls.
bs_var[0] = s0 * ncd1 - k * Math.Exp(-r * t) * ncd2;
// Calculate the pbls.
bs_var[1] = k * Math.Exp(-r * t) * npd2 - s0 * npd1;
return bs_var;
}
