/// <summary>
/// Calculates a call option on a bond.
/// </summary>
/// <param name="r0">The Zr evaluated in zero.</param>
/// <param name="t">The valuation date (in years fractions).</param>
/// <param name="T">The option exercise time to buy a bond with maturity S.</param>
/// <param name="S">The maturity of the bound to buy.</param>
/// <param name="X">The strike price.</param>
/// <param name="cirParameters">
/// A vector containing CIR model parameters k, theta, sigma.
/// </param>
/// <returns>The call option price.</returns>
public static double BondCall(double r0, double t, double T, double S, double X, Vector cirParameters)
{
double k = cirParameters[0];
double theta = cirParameters[1];
double sigma = cirParameters[2];
double h = Math.Sqrt(k * k + 2.0 * sigma * sigma);
double dentS = 2.0 * h + (k + h) * (Math.Exp(h * (S - t)) - 1.0);
double AtS = Math.Pow(2.0 * h * Math.Exp(0.5 * (k + h) * (S - t)) / dentS, 2.0 * k * theta / (sigma * sigma));
double BtS = 2.0 * (Math.Exp(h * (S - t)) - 1.0) / dentS;
double denTS = 2.0 * h + (k + h) * (Math.Exp(h * (S - T)) - 1.0);
double ATS = Math.Pow(2.0 * h * Math.Exp(0.5 * (k + h) * (S - T)) / denTS, 2.0 * k * theta / (sigma * sigma));
double BTS = 2.0 * (Math.Exp(h * (S - T)) - 1.0) / denTS;
double dentT = 2.0 * h + (k + h) * (Math.Exp(h * (T - t)) - 1.0);
double AtT = Math.Pow(2.0 * h * Math.Exp(0.5 * (k + h) * (T - t)) / dentT, 2.0 * k * theta / (sigma * sigma));
double BtT = 2.0 * (Math.Exp(h * (T - t)) - 1.0) / dentT;
double PtS = AtS * Math.Exp(-BtS * r0);
double PtT = AtT * Math.Exp(-BtT * r0);
double rstar = Math.Log(ATS / X) / BTS;
double rho = 2.0 * h / (sigma * sigma * (Math.Exp(h * (T - t)) - 1.0));
double psi = (k + h) / (sigma * sigma);
double v1 = 4.0 * k * theta / (sigma * sigma);
double v2 = 2.0 * rho * rho * r0 * Math.Exp(h * (T - t)) / (rho + psi + BTS);
double v3 = 2.0 * rho * rho * r0 * Math.Exp(h * (T - t)) / (rho + psi);
double x1 = 2.0 * rstar * (rho + psi + BTS);
double x2 = 2.0 * rstar * (rho + psi);
double c1 = v1 / 0.5 + Math.Floor(v2 / 0.5) + 1;
double c2 = v1 / 0.5 + Math.Floor(v3 / 0.5) + 1;
NonCentralChiSquare ncx21 = new NonCentralChiSquare(v1, v2);
NonCentralChiSquare ncx22 = new NonCentralChiSquare(v1, v3);
return(PtS * ncx21.Cdf(x1) - X * PtT * ncx22.Cdf(x2));
}
/// <summary>
/// Calculates a call option on a bond.
/// </summary>
/// <param name="r0">The Zr evaluated in zero.</param>
/// <param name="t">The valuation date (in years fractions).</param>
/// <param name="T">The option exercise time to buy a bond with maturity S.</param>
/// <param name="S">The maturity of the bound to buy.</param>
/// <param name="X">The strike price.</param>
/// <param name="cirParameters">
/// A vector containing CIR model parameters k, theta, sigma.
/// </param>
/// <returns>The call option price.</returns>
public static double BondCall(double r0, double t, double T, double S, double X, Vector cirParameters)
{
double k = cirParameters[0];
double theta = cirParameters[1];
double sigma = cirParameters[2];
double h = Math.Sqrt(k * k + 2.0 * sigma * sigma);
double dentS = 2.0 * h + (k + h) * (Math.Exp(h * (S - t)) - 1.0);
double AtS = Math.Pow(2.0 * h * Math.Exp(0.5 * (k + h) * (S - t)) / dentS, 2.0 * k * theta / (sigma * sigma));
double BtS = 2.0 * (Math.Exp(h * (S - t)) - 1.0) / dentS;
double denTS = 2.0 * h + (k + h) * (Math.Exp(h * (S - T)) - 1.0);
double ATS = Math.Pow(2.0 * h * Math.Exp(0.5 * (k + h) * (S - T)) / denTS, 2.0 * k * theta / (sigma * sigma));
double BTS = 2.0 * (Math.Exp(h * (S - T)) - 1.0) / denTS;
double dentT = 2.0 * h + (k + h) * (Math.Exp(h * (T - t)) - 1.0);
double AtT = Math.Pow(2.0 * h * Math.Exp(0.5 * (k + h) * (T - t)) / dentT, 2.0 * k * theta / (sigma * sigma));
double BtT = 2.0 * (Math.Exp(h * (T - t)) - 1.0) / dentT;
double PtS = AtS * Math.Exp(-BtS * r0);
double PtT = AtT * Math.Exp(-BtT * r0);
double rstar = Math.Log(ATS / X) / BTS;
double rho = 2.0 * h / (sigma * sigma * (Math.Exp(h * (T - t)) - 1.0));
double psi = (k + h) / (sigma * sigma);
double v1 = 4.0 * k * theta / (sigma * sigma);
double v2 = 2.0 * rho * rho * r0 * Math.Exp(h * (T - t)) / (rho + psi + BTS);
double v3 = 2.0 * rho * rho * r0 * Math.Exp(h * (T - t)) / (rho + psi);
double x1 = 2.0 * rstar * (rho + psi + BTS);
double x2 = 2.0 * rstar * (rho + psi);
double c1 = v1 / 0.5 + Math.Floor(v2 / 0.5) + 1;
double c2 = v1 / 0.5 + Math.Floor(v3 / 0.5) + 1;
NonCentralChiSquare ncx21 = new NonCentralChiSquare(v1, v2);
NonCentralChiSquare ncx22 = new NonCentralChiSquare(v1, v3);
return PtS * ncx21.Cdf(x1) - X * PtT * ncx22.Cdf(x2);
}
