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/*
**************************************************************
* C++ Mathematical Expression Toolkit Library *
* *
* Simple Example 15 *
* 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 <cstdio>
#include <string>
#include "exprtk.hpp"
template <typename T>
void black_scholes_merton_model()
{
typedef exprtk::symbol_table<T> symbol_table_t;
typedef exprtk::expression<T> expression_t;
typedef exprtk::parser<T> 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); "
" ";
T s = T(60.00); // Spot / Stock / Underlying / Base price
T k = T(65.00); // Strike price
T v = T( 0.30); // Volatility
T t = T( 0.25); // Years to maturity
T r = T( 0.08); // Risk free rate
std::string callput_flag;
static const T e = exprtk::details::numeric::constant::e;
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("e",e);
symbol_table.add_stringvar("callput_flag",callput_flag);
expression_t expression;
expression.register_symbol_table(symbol_table);
parser_t parser;
parser.compile(bsm_model_program,expression);
callput_flag = "call";
const T bsm_call_option_price = expression.value();
callput_flag = "put";
const T bsm_put_option_price = expression.value();
printf("BSM(call, %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n",
s, k, t, r, v,
bsm_call_option_price);
printf("BSM(put , %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n",
s, k, t, r, v,
bsm_put_option_price);
const T put_call_parity_diff =
(bsm_call_option_price - bsm_put_option_price) -
(s - k * std::exp(-r * t));
printf("Put-Call parity difference: %20.17f\n", put_call_parity_diff);
}
int main()
{
black_scholes_merton_model<double>();
return 0;
}
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