private Complex Phi(HestonProcess process, Complex a, double nu_0, double nu_t, double dt)
{
double theta = process.theta();
double kappa = process.kappa();
double sigma = process.sigma();
double sigma2 = sigma * sigma;
Complex ga = Complex.Sqrt(kappa * kappa - 2 * sigma2 * a * new Complex(0.0, 1.0));
double d = 4 * theta * kappa / sigma2;
double nu = 0.5 * d - 1;
Complex z = ga * Complex.Exp(-0.5 * ga * dt) / (1.0 - Complex.Exp(-ga * dt));
Complex log_z = -0.5 * ga * dt + Complex.Log(ga / (1.0 - Complex.Exp(-ga * dt)));
Complex alpha = 4.0 * ga * Complex.Exp(-0.5 * ga * dt) / (sigma2 * (1.0 - Complex.Exp(-ga * dt)));
Complex beta = 4.0 * kappa * Complex.Exp(-0.5 * kappa * dt) / (sigma2 * (1.0 - Complex.Exp(-kappa * dt)));
return(ga * Complex.Exp(-0.5 * (ga - kappa) * dt) * (1 - Complex.Exp(-kappa * dt))
/ (kappa * (1.0 - Complex.Exp(-ga * dt)))
* Complex.Exp((nu_0 + nu_t) / sigma2 * (
kappa * (1.0 + Complex.Exp(-kappa * dt)) / (1.0 - Complex.Exp(-kappa * dt))
- ga * (1.0 + Complex.Exp(-ga * dt)) / (1.0 - Complex.Exp(-ga * dt))))
* Complex.Exp(nu * log_z) / Complex.Pow(z, nu)
* ((nu_t > 1e-8)
? Utils.modifiedBesselFunction_i(nu, Complex.Sqrt(nu_0 * nu_t) * alpha)
/ Utils.modifiedBesselFunction_i(nu, Complex.Sqrt(nu_0 * nu_t) * beta)
: Complex.Pow(alpha / beta, nu)
));
}
