/*

**************************************************************

* C++ Mathematical Expression Toolkit Library *

* *

* Simple Example 15 *

* Author: Arash Partow (1999-2025) *

* 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;

}