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/* ************************************************************** * C++ Mathematical Expression Toolkit Library * * * * Vectorized Binomial 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 "exprtk.hpp" template void vectorized_binomial_option_pricing_model() { typedef exprtk::symbol_table symbol_table_t; typedef exprtk::expression expression_t; typedef exprtk::parser parser_t; const std::string european_option_binomial_model_program = " var dt := t / n; " " var z := exp(r * dt); " " var z_inv := 1 / z; " " var u := exp(v * sqrt(dt)); " " var u_inv := 1 / u; " " var p_up := (z - u_inv) / (u - u_inv); " " var p_down := 1 - p_up; " " " " var option_price[n + 1] := [0]; " " " " for (var i := 0; i <= n; i += 1) " " { " " var base_price := s * u^(n - 2i); " " option_price[i] := " " switch " " { " " case callput_flag == 'call' : max(base_price - k, 0); " " case callput_flag == 'put' : max(k - base_price, 0); " " }; " " }; " " " " var p_u_zinv := z_inv * p_up; " " var p_d_zinv := z_inv * p_down; " " " " for (var j := n - 1; j >= 0; j -= 1) " " { " " /* y_i <- a * x_i + b * y_(i+1) i:[0,j] */ " " axpbsy(p_u_zinv, option_price, " " p_d_zinv, 1, option_price, " " 0, j); " " }; " " " " option_price[0]; "; 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(2000.00); // Number of time steps std::string callput_flag; exprtk::rtl::vecops::package vecops_package; symbol_table_t symbol_table; 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_package(vecops_package); expression_t expression; expression.register_symbol_table(symbol_table); parser_t parser; parser.compile(european_option_binomial_model_program,expression); const std::size_t rounds = 2000; T binomial_call_option_price = T(0); T binomial_put_option_price = T(0); { callput_flag = "call"; exprtk::timer timer; timer.start(); for (std::size_t i = 0; i < rounds; ++i) { binomial_call_option_price = expression.value(); } timer.stop(); printf("BinomialOptionPrice(Type: %4s, BasePx: %5.3f, Strike: %5.3f, Time: %5.3f, RFR: %5.3f, Vol: %5.3f, Steps: %4.1f) = %10.6f " "total time: %6.3fsec rate: %6.3fcalc/sec\n", callput_flag.c_str(), s, k, t, r, v, n, binomial_call_option_price, timer.time(), rounds / timer.time()); } { callput_flag = "put"; exprtk::timer timer; timer.start(); for (std::size_t i = 0; i < rounds; ++i) { binomial_put_option_price = expression.value(); } timer.stop(); printf("BinomialOptionPrice(Type: %4s, BasePx: %5.3f, Strike: %5.3f, Time: %5.3f, RFR: %5.3f, Vol: %5.3f, Steps: %4.1f) = %10.6f " "total time: %6.3fsec rate: %6.3fcalc/sec\n", callput_flag.c_str(), s, k, t, r, v, n, binomial_put_option_price, timer.time(), rounds / timer.time()); } const T put_call_parity_diff = (binomial_call_option_price - binomial_put_option_price) - (s - k * std::exp(-r * t)); printf("Put-Call parity difference: %20.17f\n", put_call_parity_diff); } int main() { vectorized_binomial_option_pricing_model(); return 0; }