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/*
**************************************************************
* C++ Mathematical Expression Toolkit Library *
* *
* Simple Example 22 *
* 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 compute_implied_volatility()
{
typedef exprtk::symbol_table<T> symbol_table_t;
typedef exprtk::expression<T> expression_t;
typedef exprtk::parser<T> parser_t;
typedef exprtk::function_compositor<T> compositor_t;
typedef typename compositor_t::function function_t;
const std::string implied_volatility_program =
" const var epsilon := 0.0000001; "
" const var max_iters := 1000; "
" "
" var v := 0.5; /* Initial volatility guess */ "
" var itr := 0; "
" "
" while ((itr += 1) <= max_iters) "
" { "
" var price := "
" switch "
" { "
" case callput_flag == 'call' : bsm_call(s, k, r, t, v); "
" case callput_flag == 'put' : bsm_put (s, k, r, t, v); "
" }; "
" "
" var price_diff := price - target_price; "
" "
" if (abs(price_diff) <= epsilon) "
" { "
" break; "
" }; "
" "
" v -= price_diff / vega(s, k, r, t, v); "
" }; "
" "
" itr <= max_iters ? v : null; ";
T s = T( 100.00); // Spot / Stock / Underlying / Base price
T k = T( 110.00); // Strike price
T t = T( 2.22); // Years to maturity
T r = T( 0.05); // Risk free rate
T target_price = T( 0.00);
std::string callput_flag;
symbol_table_t symbol_table(symbol_table_t::e_immutable);
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_stringvar("callput_flag",callput_flag);
symbol_table.add_variable ("target_price",target_price);
symbol_table.add_pi();
compositor_t compositor(symbol_table);
compositor.add(
function_t("bsm_call")
.vars("s", "k", "r", "t", "v")
.expression
(
" var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); "
" var d2 := d1 - v * sqrt(t); "
" s * ncdf(d1) - k * exp(-r * t) * ncdf(d2); "
));
compositor.add(
function_t("bsm_put")
.vars("s", "k", "r", "t", "v")
.expression
(
" var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); "
" var d2 := d1 - v * sqrt(t); "
" k * exp(-r * t) * ncdf(-d2) - s * ncdf(-d1); "
));
compositor.add(
function_t("vega")
.vars("s", "k", "r", "t", "v")
.expression
(
" var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t)); "
" s * sqrt(t) * exp(-d1^2 / 2) / sqrt(2pi); "
));
expression_t expression;
expression.register_symbol_table(symbol_table);
parser_t parser;
parser.compile(implied_volatility_program,expression);
{
callput_flag = "call";
target_price = T(18.339502);
const T implied_vol = expression.value();
printf("Call Option(s: %5.3f, k: %5.3f, t: %5.3f, r: %5.3f) "
"@ $%8.6f Implied volatility = %10.8f\n",
s, k, t, r, target_price, implied_vol);
}
{
callput_flag = "put";
target_price = T(16.782764);
const T implied_vol = expression.value();
printf("Put Option(s: %5.3f, k: %5.3f, t: %5.3f, r: %5.3f) "
"@ $%8.6f Implied volatility = %10.8f\n",
s, k, t, r, target_price, implied_vol);
}
}
int main()
{
compute_implied_volatility<double>();
return 0;
}
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