ceph/src/boost/libs/math/example/autodiff_black_scholes_brief.cpp

   1 //           Copyright Matthew Pulver 2018 - 2019.
   2 // Distributed under the Boost Software License, Version 1.0.
   3 //      (See accompanying file LICENSE_1_0.txt or copy at
   4 //           https://www.boost.org/LICENSE_1_0.txt)
   5
   6 #include <boost/math/differentiation/autodiff.hpp>
   7 #include <iostream>
   8 #include <stdexcept>
   9
  10 using namespace boost::math::constants;
  11 using namespace boost::math::differentiation;
  12
  13 // Equations and function/variable names are from
  14 // https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
  15
  16 // Standard normal cumulative distribution function
  17 template <typename X>
  18 X Phi(X const& x) {
  19   return 0.5 * erfc(-one_div_root_two<X>() * x);
  20 }
  21
  22 enum class CP { call, put };
  23
  24 // Assume zero annual dividend yield (q=0).
  25 template <typename Price, typename Sigma, typename Tau, typename Rate>
  26 promote<Price, Sigma, Tau, Rate> black_scholes_option_price(CP cp,
  27                                                             double K,
  28                                                             Price const& S,
  29                                                             Sigma const& sigma,
  30                                                             Tau const& tau,
  31                                                             Rate const& r) {
  32   using namespace std;
  33   auto const d1 = (log(S / K) + (r + sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
  34   auto const d2 = (log(S / K) + (r - sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
  35   switch (cp) {
  36     case CP::call:
  37       return S * Phi(d1) - exp(-r * tau) * K * Phi(d2);
  38     case CP::put:
  39       return exp(-r * tau) * K * Phi(-d2) - S * Phi(-d1);
  40     default:
  41       throw std::runtime_error("Invalid CP value.");
  42   }
  43 }
  44
  45 int main() {
  46   double const K = 100.0;                    // Strike price.
  47   auto const S = make_fvar<double, 2>(105);  // Stock price.
  48   double const sigma = 5;                    // Volatility.
  49   double const tau = 30.0 / 365;             // Time to expiration in years. (30 days).
  50   double const r = 1.25 / 100;               // Interest rate.
  51   auto const call_price = black_scholes_option_price(CP::call, K, S, sigma, tau, r);
  52   auto const put_price = black_scholes_option_price(CP::put, K, S, sigma, tau, r);
  53
  54   std::cout << "black-scholes call price = " << call_price.derivative(0) << '\n'
  55             << "black-scholes put  price = " << put_price.derivative(0) << '\n'
  56             << "call delta = " << call_price.derivative(1) << '\n'
  57             << "put  delta = " << put_price.derivative(1) << '\n'
  58             << "call gamma = " << call_price.derivative(2) << '\n'
  59             << "put  gamma = " << put_price.derivative(2) << '\n';
  60   return 0;
  61 }
  62 /*
  63 Output:
  64 black-scholes call price = 56.5136
  65 black-scholes put  price = 51.4109
  66 call delta = 0.773818
  67 put  delta = -0.226182
  68 call gamma = 0.00199852
  69 put  gamma = 0.00199852
  70 **/