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/* ************************************************************** * C++ Mathematical Expression Toolkit Library * * * * ExprTk Black Scholes Merton Benchmark * * 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" static const std::size_t rounds = 20000000; template struct bsm_parameters { T s; // Spot / Stock / Underlying / Base price T k; // Strike price T v; // Volatility T t; // Years to maturity T r; // Risk free rate }; const bsm_parameters bsm_list[] = { { 60.11, 65.11, 0.31, 0.25, 0.08 }, { 60.22, 65.22, 0.32, 0.35, 0.07 }, { 60.33, 65.33, 0.33, 0.45, 0.06 }, { 60.44, 65.44, 0.34, 0.55, 0.05 }, { 60.55, 65.55, 0.35, 0.65, 0.04 }, { 60.66, 65.66, 0.36, 0.75, 0.03 }, { 60.77, 65.77, 0.37, 0.85, 0.08 }, { 60.88, 65.88, 0.38, 0.95, 0.07 }, { 60.11, 65.11, 0.31, 0.25, 0.06 }, { 60.22, 65.22, 0.32, 0.35, 0.05 }, { 60.33, 65.33, 0.33, 0.45, 0.04 }, { 60.44, 65.44, 0.34, 0.55, 0.03 }, { 60.55, 65.55, 0.35, 0.65, 0.08 }, { 60.66, 65.66, 0.36, 0.75, 0.07 }, { 60.77, 65.77, 0.37, 0.85, 0.06 }, { 60.88, 65.88, 0.38, 0.95, 0.05 } }; const std::size_t bsm_list_size = sizeof (bsm_list) / sizeof(bsm_parameters); template inline T call_bsm_model(T s, T k, T t, T r, T v) { using namespace std; using namespace exprtk::details::numeric; const T d1 = (log(s / k) + (r + (v * v) / 2) * t) / (v * sqrt(t)); const T d2 = d1 - v * sqrt(t); return s * ncdf(d1) - k * exp(-r * t) * ncdf(d2); } template inline T put_bsm_model(T s, T k, T t, T r, T v) { using namespace std; using namespace exprtk::details::numeric; const T d1 = (log(s / k) + (r + (v * v) / 2) * t) / (v * sqrt(t)); const T d2 = d1 - v * sqrt(t); return k * exp(-r * t) * ncdf(-d2) - s * ncdf(-d1); } template void black_scholes_merton_model() { typedef exprtk::symbol_table symbol_table_t; typedef exprtk::expression expression_t; typedef exprtk::parser parser_t; const std::string bsm_model_program = " var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); " " var d2 := d1 - v * sqrt(t); " " " " if (callput_flag == 'call') " " s * ncdf(d1) - k * e^(-r * t) * ncdf(d2); " " else if (callput_flag == 'put') " " k * e^(-r * t) * ncdf(-d2) - s * ncdf(-d1); " " "; const std::string bsm_model_program_opt1 = " var v_sqrtt := (v * sqrt(t)); " " var d1 := (log(s / k) + (r + v * v / 2) * t) / v_sqrtt; " " var d2 := d1 - v_sqrtt; " " var kert := k * exp(-r * t); " " " " if (callput_flag == 'call') " " s * ncdf(d1) - kert * ncdf(d2); " " else if (callput_flag == 'put') " " kert * ncdf(-d2) - s * ncdf(-d1); " " "; const std::string bsm_model_program_opt2 = " var v_sqrtt := (v * sqrt(t)); " " var d1 := (log(s / k) + (r + v * v / 2) * t) / v_sqrtt; " " var d2 := d1 - v_sqrtt; " " " " if (callput_flag == 'call') " " s * ncdf(d1) - (k * exp(-r * t)) * ncdf(d2); " " else if (callput_flag == 'put') " " (k * exp(-r * t)) * ncdf(-d2) - s * ncdf(-d1); " " "; const std::string bsm_model_program_opt3 = " if (callput_flag == 'call') " " call_bsm_model(s, k, t, r, v); " " else if (callput_flag == 'put') " " put_bsm_model(s, k, t, r, v); " " "; bsm_parameters parameters; std::string callput_flag; static const T e = exprtk::details::numeric::constant::e; symbol_table_t symbol_table; symbol_table.add_variable ( "s", parameters.s ); symbol_table.add_variable ( "k", parameters.k ); symbol_table.add_variable ( "t", parameters.t ); symbol_table.add_variable ( "r", parameters.r ); symbol_table.add_variable ( "v", parameters.v ); symbol_table.add_constant ( "e", e ); symbol_table.add_stringvar( "callput_flag" , callput_flag ); symbol_table.add_function ( "call_bsm_model", call_bsm_model ); symbol_table.add_function ( "put_bsm_model" , put_bsm_model ); expression_t bsm_expression (symbol_table); expression_t bsm_expression_opt1(symbol_table); expression_t bsm_expression_opt2(symbol_table); expression_t bsm_expression_opt3(symbol_table); parser_t parser; parser.compile(bsm_model_program , bsm_expression ); parser.compile(bsm_model_program_opt1, bsm_expression_opt1); parser.compile(bsm_model_program_opt2, bsm_expression_opt2); parser.compile(bsm_model_program_opt3, bsm_expression_opt3); { exprtk::timer timer; timer.start(); T total = T(0); for (std::size_t i = 0; i < rounds; ++i) { const bsm_parameters& current_parameters = bsm_list[i % bsm_list_size]; parameters = current_parameters; callput_flag = "call"; total += bsm_expression.value(); callput_flag = "put"; total += bsm_expression.value(); } timer.stop(); printf("[exprtk0] Total: %13.5f Time:%6.3fsec Rate:%13.3fbsm/sec execrt: %6.3fns\n", total, timer.time(), (2.0 * rounds) / timer.time(), 1e9 / ((2.0 * rounds) / timer.time())); } { exprtk::timer timer; timer.start(); T total = T(0); for (std::size_t i = 0; i < rounds; ++i) { const bsm_parameters& current_parameters = bsm_list[i % bsm_list_size]; parameters = current_parameters; callput_flag = "call"; total += bsm_expression_opt1.value(); callput_flag = "put"; total += bsm_expression_opt1.value(); } timer.stop(); printf("[exprtk1] Total: %13.5f Time:%6.3fsec Rate:%13.3fbsm/sec execrt: %6.3fns\n", total, timer.time(), (2.0 * rounds) / timer.time(), 1e9 / ((2.0 * rounds) / timer.time())); } { exprtk::timer timer; timer.start(); T total = T(0); for (std::size_t i = 0; i < rounds; ++i) { const bsm_parameters& current_parameters = bsm_list[i % bsm_list_size]; parameters = current_parameters; callput_flag = "call"; total += bsm_expression_opt2.value(); callput_flag = "put"; total += bsm_expression_opt2.value(); } timer.stop(); printf("[exprtk2] Total: %13.5f Time:%6.3fsec Rate:%13.3fbsm/sec execrt: %6.3fns\n", total, timer.time(), (2.0 * rounds) / timer.time(), 1e9 / ((2.0 * rounds) / timer.time())); } { exprtk::timer timer; timer.start(); T total = T(0); for (std::size_t i = 0; i < rounds; ++i) { const bsm_parameters& current_parameters = bsm_list[i % bsm_list_size]; parameters = current_parameters; callput_flag = "call"; total += bsm_expression_opt3.value(); callput_flag = "put"; total += bsm_expression_opt3.value(); } timer.stop(); printf("[exprtk3] Total: %13.5f Time:%6.3fsec Rate:%13.3fbsm/sec execrt: %6.3fns\n", total, timer.time(), (2.0 * rounds) / timer.time(), 1e9 / ((2.0 * rounds) / timer.time())); } } template inline T bsm_model(const std::string& callput_flag, const T s, const T k, const T t, const T r, const T v) { using namespace std; using namespace exprtk::details::numeric; const T d1 = (log(s / k) + (r + (v * v) / 2) * t) / (v * sqrt(t)); const T d2 = d1 - v * sqrt(t); if (callput_flag == "call") return s * ncdf(d1) - k * exp(-r * t) * ncdf(d2); else if (callput_flag == "put") return k * exp(-r * t) * ncdf(-d2) - s * ncdf(-d1); else return T(0); } template void bsm_native() { bsm_parameters parameters; std::string callput_flag; exprtk::timer timer; timer.start(); T total = T(0); for (std::size_t i = 0; i < rounds; ++i) { const bsm_parameters& current_parameters = bsm_list[i % bsm_list_size]; parameters = current_parameters; callput_flag = "call"; total += bsm_model(callput_flag, parameters.s, parameters.k, parameters.t, parameters.r, parameters.v); callput_flag = "put"; total += bsm_model(callput_flag, parameters.s, parameters.k, parameters.t, parameters.r, parameters.v); } timer.stop(); printf("[native ] Total: %13.5f Time:%6.3fsec Rate:%13.3fbsm/sec execrt: %6.3fns\n", total, timer.time(), (2.0 * rounds) / timer.time(), 1e9 / ((2.0 * rounds) / timer.time())); } int main() { black_scholes_merton_model(); bsm_native(); return 0; } /* Build command: c++ -pedantic-errors -Wall -Wextra -Werror -flto -march=native -O3 -DNDEBUG -o exprtk_bsm_benchmark exprtk_bsm_benchmark.cpp -L/usr/lib -lstdc++ -lm */