153 lines
6.3 KiB
C++
153 lines
6.3 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 22 *
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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 compute_option_implied_volatility()
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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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typedef exprtk::function_compositor<T> compositor_t;
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typedef typename compositor_t::function function_t;
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const std::string option_implied_volatility_program =
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" const var epsilon := 0.0000001; "
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" const var max_iters := 1000; "
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" "
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" var v := 0.5; /* Initial volatility guess */ "
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" var itr := 0; "
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" "
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" while ((itr += 1) <= max_iters) "
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" { "
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" var price := "
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" switch "
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" { "
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" case callput_flag == 'call' : bsm_call(s, k, r, t, v); "
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" case callput_flag == 'put' : bsm_put (s, k, r, t, v); "
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" }; "
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" "
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" var price_diff := price - target_price; "
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" "
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" if (abs(price_diff) <= epsilon) "
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" { "
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" break; "
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" }; "
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" "
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" var vega := bsm_vega(s, k, r, t, v); "
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" "
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" if (vega < epsilon) "
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" { "
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" itr := max_iters + 1; "
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" break; "
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" }; "
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" "
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" v -= price_diff / vega; "
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" }; "
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" "
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" itr <= max_iters ? v : null; ";
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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 t = T( 2.22); // Years to maturity
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T r = T( 0.05); // Risk free rate
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T target_price = T( 0.00);
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std::string callput_flag;
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symbol_table_t symbol_table(symbol_table_t::e_immutable);
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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_stringvar("callput_flag",callput_flag);
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symbol_table.add_variable ("target_price",target_price);
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symbol_table.add_pi();
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compositor_t compositor(symbol_table);
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compositor.add(
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function_t("bsm_call")
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.vars("s", "k", "r", "t", "v")
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.expression
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(
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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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" s * ncdf(d1) - k * exp(-r * t) * ncdf(d2); "
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));
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compositor.add(
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function_t("bsm_put")
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.vars("s", "k", "r", "t", "v")
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.expression
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(
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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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" k * exp(-r * t) * ncdf(-d2) - s * ncdf(-d1); "
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));
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compositor.add(
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function_t("bsm_vega")
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.vars("s", "k", "r", "t", "v")
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.expression
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(
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" var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); "
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" s * sqrt(t) * exp(-d1^2 / 2) / sqrt(2pi); "
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));
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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(option_implied_volatility_program, expression);
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{
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callput_flag = "call";
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target_price = T(18.339502);
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const T option_implied_vol = expression.value();
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printf("Call Option(s: %5.3f, k: %5.3f, t: %5.3f, r: %5.3f) "
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"@ $%8.6f Implied volatility = %10.8f\n",
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s, k, t, r, target_price, option_implied_vol);
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}
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{
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callput_flag = "put";
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target_price = T(16.782764);
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const T option_implied_vol = expression.value();
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printf("Put Option(s: %5.3f, k: %5.3f, t: %5.3f, r: %5.3f) "
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"@ $%8.6f Implied volatility = %10.8f\n",
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s, k, t, r, target_price, option_implied_vol);
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}
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}
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int main()
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{
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compute_option_implied_volatility<double>();
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return 0;
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}
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