118 lines
5.1 KiB
C++
118 lines
5.1 KiB
C++
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/*
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**************************************************************
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* C++ Mathematical Expression Toolkit Library *
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* *
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* Simple Example 21 *
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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 binomial_option_pricing_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 european_option_binomial_model_program =
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" var dt := t / n; "
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" var z := exp(r * dt); "
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" var z_inv := 1 / z; "
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" var u := exp(v * sqrt(dt)); "
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" var u_inv := 1 / u; "
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" var p_up := (z - u_inv) / (u - u_inv); "
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" var p_down := 1 - p_up; "
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" "
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" var option_price[n + 1] := [0]; "
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" "
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" for (var i := 0; i <= n; i += 1) "
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" { "
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" var base_price := s * u^(n - 2i); "
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" option_price[i] := "
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" switch "
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" { "
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" case callput_flag == 'call' : max(base_price - k, 0); "
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" case callput_flag == 'put' : max(k - base_price, 0); "
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" }; "
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" }; "
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" "
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" for (var j := n - 1; j >= 0; j -= 1) "
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" { "
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" for (var i := 0; i <= j; i += 1) "
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" { "
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" option_price[i] := z_inv * "
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" (p_up * option_price[i] + p_down * option_price[i + 1]); "
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" } "
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" }; "
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" "
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" option_price[0]; ";
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T s = T( 100.00); // Spot / Stock / Underlying / Base price
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T k = T( 110.00); // Strike price
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T v = T( 0.30); // Volatility
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T t = T( 2.22); // Years to maturity
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T r = T( 0.05); // Risk free rate
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T n = T(1000.00); // Number of time steps
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std::string callput_flag;
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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("n",n);
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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(european_option_binomial_model_program,expression);
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callput_flag = "call";
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const T binomial_call_option_price = expression.value();
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callput_flag = "put";
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const T binomial_put_option_price = expression.value();
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printf("BinomialPrice(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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binomial_call_option_price);
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printf("BinomialPrice(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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binomial_put_option_price);
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const T put_call_parity_diff =
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(binomial_call_option_price - binomial_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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binomial_option_pricing_model<double>();
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return 0;
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}
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