Black-Scholes option pricing

BlackScholes.cpp

#include <cmath>
#include <tuple>

// mostly taken from http://www.espenhaug.com/black_scholes.html

// the cumulative normal distribution function
auto CND(double value)
{
    return 0.5 * std::erfc(-value * M_SQRT1_2);
}

// Black-Scholes (1973) formula
// S: stock price
// X: strike price
// T: years to maturity
// r: risk-free rate
// v: volatility
auto BlackScholes(double S, double X, double T, double R, double V)
{
    const auto sqrtT = std::sqrt(T);

    const auto d1 = (std::log(S / X) + (R + 0.5 * V * V) * T) / (V * sqrtT);
    const auto d2 = d1 - V * sqrtT;
    const auto CNDD1 = CND(d1);
    const auto CNDD2 = CND(d2);

    const auto expRT = std::exp(-R * T);

    const auto call = S * CNDD1 - X * expRT * CNDD2;
    const auto put = X * expRT * (1.0 - CNDD2) - S * (1.0 - CNDD1);

    return std::make_tuple(call, put);
}

#include <iostream>
#include <iomanip>

int main()
{
    double call, put;
    std::tie(call, put) = BlackScholes(10, 12, 1, 0.003, 0.4);
    std::cout << std::fixed << std::setprecision(4) << call << ' ' << put << '\n';
    // expected: 0.9291 2.8921
}