96 lines
3.2 KiB
C++
96 lines
3.2 KiB
C++
/*
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**************************************************************
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* C++ Mathematical Expression Toolkit Library *
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* *
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* Simple Example 15 *
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* Author: Arash Partow (1999-2024) *
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* URL: https://www.partow.net/programming/exprtk/index.html *
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* *
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* Copyright notice: *
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* Free use of the Mathematical Expression Toolkit Library is *
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* permitted under the guidelines and in accordance with the *
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* most current version of the MIT License. *
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* https://www.opensource.org/licenses/MIT *
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* SPDX-License-Identifier: MIT *
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* *
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**************************************************************
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*/
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#include <cstdio>
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#include <string>
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#include "exprtk.hpp"
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template <typename T>
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void black_scholes_merton_model()
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{
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typedef exprtk::symbol_table<T> symbol_table_t;
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typedef exprtk::expression<T> expression_t;
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typedef exprtk::parser<T> parser_t;
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const std::string bsm_model_program =
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" var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); "
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" var d2 := d1 - v * sqrt(t); "
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" "
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" if (callput_flag == 'call') "
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" s * ncdf(d1) - k * e^(-r * t) * ncdf(d2); "
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" else if (callput_flag == 'put') "
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" k * e^(-r * t) * ncdf(-d2) - s * ncdf(-d1); "
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" ";
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T s = T(60.00); // Spot / Stock / Underlying / Base price
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T k = T(65.00); // Strike price
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T v = T( 0.30); // Volatility
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T t = T( 0.25); // Years to maturity
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T r = T( 0.08); // Risk free rate
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std::string callput_flag;
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static const T e = exprtk::details::numeric::constant::e;
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symbol_table_t symbol_table;
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symbol_table.add_variable("s",s);
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symbol_table.add_variable("k",k);
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symbol_table.add_variable("t",t);
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symbol_table.add_variable("r",r);
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symbol_table.add_variable("v",v);
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symbol_table.add_constant("e",e);
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symbol_table.add_stringvar("callput_flag",callput_flag);
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expression_t expression;
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expression.register_symbol_table(symbol_table);
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parser_t parser;
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parser.compile(bsm_model_program,expression);
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callput_flag = "call";
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const T bsm_call_option_price = expression.value();
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callput_flag = "put";
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const T bsm_put_option_price = expression.value();
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printf("BSM(call, %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n",
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s, k, t, r, v,
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bsm_call_option_price);
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printf("BSM(put , %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n",
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s, k, t, r, v,
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bsm_put_option_price);
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const T put_call_parity_diff =
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(bsm_call_option_price - bsm_put_option_price) -
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(s - k * std::exp(-r * t));
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printf("Put-Call parity difference: %20.17f\n", put_call_parity_diff);
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}
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int main()
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{
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black_scholes_merton_model<double>();
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return 0;
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}
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