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/* ************************************************************** * C++ Mathematical Expression Toolkit Library * * * * ExprTk Monte-Carlo Based European Option Pricing Model * * Author: Arash Partow (1999-2024) * * URL: https://www.partow.net/programming/exprtk/index.html * * * * Copyright notice: * * Free use of the Mathematical Expression Toolkit Library is * * permitted under the guidelines and in accordance with the * * most current version of the MIT License. * * https://www.opensource.org/licenses/MIT * * SPDX-License-Identifier: MIT * * * ************************************************************** */ #include #include #include #include #include #include "exprtk.hpp" template struct normal_distribution final : public exprtk::ifunction{ using exprtk::ifunction::operator(); normal_distribution() : exprtk::ifunction(2) { std::random_device device; std::array seed; std::generate_n(seed.data(), seed.size(), std::ref(device)); std::seed_seq seq(std::begin(seed), std::end(seed)); generator.seed(seq); } inline T operator()(const T& mean, const T& stddev) override { std::normal_distribution distribution{mean, stddev}; return distribution(generator); } std::mt19937 generator; }; template void exprtk_montecarlo_option_pricing_model() { typedef exprtk::symbol_table symbol_table_t; typedef exprtk::expression expression_t; typedef exprtk::parser parser_t; const std::string exprtk_montecarlo_option_pricing_model_program = " var payoff_sum := 0; " " var sqrt_t := sqrt(t); " " " " for (var i := 0; i < n; i += 1) " " { " " var s_t := s * exp((r - v^2 / 2) * t + v * sqrt_t * normal(0,1)); " " payoff_sum += " " switch " " { " " case callput_flag == 'call' : max(s_t - k, 0); " " case callput_flag == 'put' : max(k - s_t, 0); " " }; " " }; " " " " exp(-r * t) * payoff_sum / n; "; T s = T(100.00); // Spot / Stock / Underlying / Base price T k = T(110.00); // Strike price T v = T( 0.30); // Volatility T t = T( 2.22); // Years to maturity T r = T( 0.05); // Risk free rate T n = T( 2.0e7); // Number of simulations std::string callput_flag; normal_distribution normal; symbol_table_t symbol_table(symbol_table_t::e_immutable); symbol_table.add_variable("s",s); symbol_table.add_variable("k",k); symbol_table.add_variable("t",t); symbol_table.add_variable("r",r); symbol_table.add_variable("v",v); symbol_table.add_constant("n",n); symbol_table.add_stringvar("callput_flag", callput_flag); symbol_table.add_function ("normal" , normal ); expression_t expression; expression.register_symbol_table(symbol_table); parser_t parser; parser.compile(exprtk_montecarlo_option_pricing_model_program, expression); callput_flag = "call"; const T montecarlo_call_option_price = expression.value(); callput_flag = "put"; const T montecarlo_put_option_price = expression.value(); printf("MCOptionPrice(call, %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n", s, k, t, r, v, montecarlo_call_option_price); printf("MCOptionPrice(put , %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n", s, k, t, r, v, montecarlo_put_option_price); const double put_call_parity_diff = (montecarlo_call_option_price - montecarlo_put_option_price) - (s - k * std::exp(-r * t)); printf("Put-Call parity difference: %20.17f\n", put_call_parity_diff); } int main() { exprtk_montecarlo_option_pricing_model(); return 0; }