black_scholes.hpp

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#pragma once
 
#include <cmath>
 
namespace quant::bs {
 
inline double normal_pdf(double x) {
    static constexpr double INV_SQRT_2PI = 0.39894228040143267794; // 1/sqrt(2*pi)
    return INV_SQRT_2PI * std::exp(-0.5 * x * x);
}
 
inline double normal_cdf(double x) { return 0.5 * std::erfc(-x / std::sqrt(2.0)); }
 
struct Params {
    double spot;     // S
    double strike;   // K
    double rate;     // r (risk-free rate)
    double dividend; // q (continuous dividend yield)
    double vol;      // sigma
    double time;     // T (years)
};
 
inline double d1(double S, double K, double r, double q, double sigma, double T) {
    const double vol_sqrt_t = sigma * std::sqrt(T);
    return (std::log(S / K) + (r - q + 0.5 * sigma * sigma) * T) / vol_sqrt_t;
}
 
inline double d2(double d1_value, double sigma, double T) { return d1_value - sigma * std::sqrt(T); }
 
 
double call_price(double S, double K, double r, double q, double sigma, double T);
 
 
double put_price(double S, double K, double r, double q, double sigma, double T);
 
inline double call_price(const Params& p) {
    return call_price(p.spot, p.strike, p.rate, p.dividend, p.vol, p.time);
}
 
inline double put_price(const Params& p) {
    return put_price(p.spot, p.strike, p.rate, p.dividend, p.vol, p.time);
}
 
double delta_call(double S, double K, double r, double q, double sigma, double T);
double delta_put(double S, double K, double r, double q, double sigma, double T);
double gamma(double S, double K, double r, double q, double sigma, double T);
double vega(double S, double K, double r, double q, double sigma, double T);
double theta_call(double S, double K, double r, double q, double sigma, double T);
double theta_put(double S, double K, double r, double q, double sigma, double T);
double rho_call(double S, double K, double r, double q, double sigma, double T);
double rho_put(double S, double K, double r, double q, double sigma, double T);
 
double implied_vol_call(double S, double K, double r, double q, double T, double price);
double implied_vol_put(double S, double K, double r, double q, double T, double price);
 
} // namespace quant::bs