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/*
**************************************************************
* C++ Mathematical Expression Toolkit Library *
* *
* Simple Example 21 *
* 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 binomial_option_pricing_model()
{
typedef exprtk::symbol_table<T> symbol_table_t;
typedef exprtk::expression<T> expression_t;
typedef exprtk::parser<T> parser_t;
const std::string european_option_binomial_model_program =
" var dt := t / n; "
" var z := exp(r * dt); "
" var z_inv := 1 / z; "
" var u := exp(v * sqrt(dt)); "
" var u_inv := 1 / u; "
" var p_up := (z - u_inv) / (u - u_inv); "
" var p_down := 1 - p_up; "
" "
" var option_price[n + 1] := [0]; "
" "
" for (var i := 0; i <= n; i += 1) "
" { "
" var base_price := s * u^(n - 2i); "
" option_price[i] := "
" switch "
" { "
" case callput_flag == 'call' : max(base_price - k, 0); "
" case callput_flag == 'put' : max(k - base_price, 0); "
" }; "
" }; "
" "
" for (var j := n - 1; j >= 0; j -= 1) "
" { "
" for (var i := 0; i <= j; i += 1) "
" { "
" option_price[i] := z_inv * "
" (p_up * option_price[i] + p_down * option_price[i + 1]); "
" } "
" }; "
" "
" option_price[0]; ";
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 n = T(1000.00); // Number of time steps
std::string callput_flag;
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("n",n);
symbol_table.add_stringvar("callput_flag",callput_flag);
expression_t expression;
expression.register_symbol_table(symbol_table);
parser_t parser;
parser.compile(european_option_binomial_model_program,expression);
callput_flag = "call";
const T binomial_call_option_price = expression.value();
callput_flag = "put";
const T binomial_put_option_price = expression.value();
printf("BinomialPrice(call, %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n",
s, k, t, r, v,
binomial_call_option_price);
printf("BinomialPrice(put , %5.3f, %5.3f, %5.3f, %5.3f, %5.3f) = %10.6f\n",
s, k, t, r, v,
binomial_put_option_price);
const T put_call_parity_diff =
(binomial_call_option_price - binomial_put_option_price) -
(s - k * std::exp(-r * t));
printf("Put-Call parity difference: %20.17f\n", put_call_parity_diff);
}
int main()
{
binomial_option_pricing_model<double>();
return 0;
}
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