SimMethod/analytic.cpp at master · Baptiste56/SimMethod · GitHub

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#include "analytic.h"

namespace GBM {
    namespace Analytic {

        double norm_pdf(const double &x) {
            return (1.0 / (pow(2 * M_PI, 0.5))) * exp(-0.5 * x * x);
        }

        double norm_cdf(const double &x) {
            double k = 1.0 / (1.0 + 0.2316419 * x);
            double k_sum =
                    k * (0.319381530 + k * (-0.356563782 + k * (1.781477937 + k * (-1.821255978 + 1.330274429 * k))));

            if (x >= 0.0) {
                return (1.0 - (1.0 / (pow(2 * M_PI, 0.5))) * exp(-0.5 * x * x) * k_sum);
            } else {
                return 1.0 - norm_cdf(-x);
            }
        }

        double d_j(const int &j, const double &S, const double &K, const double &r, const double &v, const double &T) {
            return (log(S / K) + (r + (pow(-1, j - 1)) * 0.5 * v * v) * T) / (v * (pow(T, 0.5)));
        }

        double call_price(const double &S, const double &K, const double &r, const double &v, const double &T) {
            return S * norm_cdf(d_j(1, S, K, r, v, T)) - K * exp(-r * T) * norm_cdf(d_j(2, S, K, r, v, T));
        }

        double call_delta(const double &S, const double &K, const double &r, const double &v, const double &T) {
            return norm_cdf(d_j(1, S, K, r, v, T));
        }

        double call_gamma(const double &S, const double &K, const double &r, const double &v, const double &T) {
            return norm_pdf(d_j(1, S, K, r, v, T)) / (S * v * sqrt(T));
        }

        double call_vega(const double &S, const double &K, const double &r, const double &v, const double &T) {
            return S * norm_pdf(d_j(1, S, K, r, v, T)) * sqrt(T);
        }
    }
}