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/* ************************************************************** * C++ Mathematical Expression Toolkit Library * * * * Merton Jump Diffusion Process 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 european_option_merton_jump_diffusion_process() { typedef exprtk::symbol_table symbol_table_t; typedef exprtk::expression expression_t; typedef exprtk::parser parser_t; typedef exprtk::function_compositor compositor_t; typedef typename compositor_t::function function_t; const std::string european_option_merton_jump_diffusion_process_program = " var lambda_t := lambda * t; " " var v_sqr := v^2; " " var sigmaJ_sqr := sigmaJ^2; " " " " var option_price := 0; " " var factorial := 1; " " " " for (var i := 0; i < n; i += 1) " " { " " var prob := exp(-lambda_t) * lambda_t^i / factorial; " " var r_i := r - lambda * muJ + (i / t) * log(1 + muJ); " " var sigma_i := sqrt(v_sqr + (i * sigmaJ_sqr) / t); " " " " option_price += " " switch " " { " " case callput_flag == 'call' : prob * bsm_call(s, k, r_i, t, sigma_i); " " case callput_flag == 'put' : prob * bsm_put (s, k, r_i, t, sigma_i); " " }; " " " " factorial *= (i > 1) ? i : 1; " " }; " " " " option_price; "; 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 lambda = T(0.0001); // Jump intensity (average jumps per year) T muJ = T( -0.05); // Mean jump size (negative for downward jumps) T sigmaJ = T( 0.30); // Standard deviation of the jump size T n = T( 50.00); // Number of terms in the Poisson sum std::string callput_flag; 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 ("v" , v ); symbol_table.add_variable ("t" , t ); symbol_table.add_variable ("r" , r ); symbol_table.add_variable ("lambda", lambda); symbol_table.add_variable ("muJ" , muJ ); symbol_table.add_variable ("sigmaJ", sigmaJ); symbol_table.add_variable ("n" , n ); symbol_table.add_stringvar("callput_flag",callput_flag); symbol_table.add_pi(); compositor_t compositor(symbol_table); compositor.add( function_t("bsm_call") .vars("s", "k", "r", "t", "v") .expression ( " var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); " " var d2 := d1 - v * sqrt(t); " " s * ncdf(d1) - k * exp(-r * t) * ncdf(d2); " )); compositor.add( function_t("bsm_put") .vars("s", "k", "r", "t", "v") .expression ( " var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); " " var d2 := d1 - v * sqrt(t); " " k * exp(-r * t) * ncdf(-d2) - s * ncdf(-d1); " )); expression_t expression; expression.register_symbol_table(symbol_table); parser_t parser; parser.compile(european_option_merton_jump_diffusion_process_program, expression); callput_flag = "call"; const T jdp_call_option_price = expression.value(); callput_flag = "put"; const T jdp_put_option_price = expression.value(); printf("JDPPrice(%4s, %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n", "call", s, k, t, r, v, jdp_call_option_price); printf("JDPPrice(%4s, %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n", "put", s, k, t, r, v, jdp_put_option_price); const T put_call_parity_diff = (jdp_call_option_price - jdp_put_option_price) - (s - k * std::exp(-r * t)); printf("Put-Call parity difference: %20.17f\n", put_call_parity_diff); } int main() { european_option_merton_jump_diffusion_process(); return 0; }