EQ2EMu/EQ2/source/depends/boost_1_72_0/libs/math/example/autodiff_black_scholes_brief.cpp

//           Copyright Matthew Pulver 2018 - 2019.
// Distributed under the Boost Software License, Version 1.0.
//      (See accompanying file LICENSE_1_0.txt or copy at
//           https://www.boost.org/LICENSE_1_0.txt)

#include <boost/math/differentiation/autodiff.hpp>
#include <iostream>
#include <stdexcept>

using namespace boost::math::constants;
using namespace boost::math::differentiation;

// Equations and function/variable names are from
// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks

// Standard normal cumulative distribution function
template <typename X>
X Phi(X const& x) {
  return 0.5 * erfc(-one_div_root_two<X>() * x);
}

enum class CP { call, put };

// Assume zero annual dividend yield (q=0).
template <typename Price, typename Sigma, typename Tau, typename Rate>
promote<Price, Sigma, Tau, Rate> black_scholes_option_price(CP cp,
                                                            double K,
                                                            Price const& S,
                                                            Sigma const& sigma,
                                                            Tau const& tau,
                                                            Rate const& r) {
  using namespace std;
  auto const d1 = (log(S / K) + (r + sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
  auto const d2 = (log(S / K) + (r - sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
  switch (cp) {
    case CP::call:
      return S * Phi(d1) - exp(-r * tau) * K * Phi(d2);
    case CP::put:
      return exp(-r * tau) * K * Phi(-d2) - S * Phi(-d1);
    default:
      throw std::runtime_error("Invalid CP value.");
  }
}

int main() {
  double const K = 100.0;                    // Strike price.
  auto const S = make_fvar<double, 2>(105);  // Stock price.
  double const sigma = 5;                    // Volatility.
  double const tau = 30.0 / 365;             // Time to expiration in years. (30 days).
  double const r = 1.25 / 100;               // Interest rate.
  auto const call_price = black_scholes_option_price(CP::call, K, S, sigma, tau, r);
  auto const put_price = black_scholes_option_price(CP::put, K, S, sigma, tau, r);

  std::cout << "black-scholes call price = " << call_price.derivative(0) << '\n'
            << "black-scholes put  price = " << put_price.derivative(0) << '\n'
            << "call delta = " << call_price.derivative(1) << '\n'
            << "put  delta = " << put_price.derivative(1) << '\n'
            << "call gamma = " << call_price.derivative(2) << '\n'
            << "put  gamma = " << put_price.derivative(2) << '\n';
  return 0;
}
/*
Output:
black-scholes call price = 56.5136
black-scholes put  price = 51.4109
call delta = 0.773818
put  delta = -0.226182
call gamma = 0.00199852
put  gamma = 0.00199852
**/