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exprtk/exprtk_simple_example_22.cpp at master · ArashPartow/exprtk · GitHub
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/*
**************************************************************
* C++ Mathematical Expression Toolkit Library *
* *
* Simple Example 22 *
* 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
compute_european_option_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 option_implied_volatility_program =
"
const var epsilon := 0.0000001;
"
"
const var max_iters := 1000;
"
"
"
"
var vola := 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, vola);
"
"
case callput_flag == 'put' : bsm_put (s, k, r, t, vola);
"
"
};
"
"
"
"
var price_diff := price - target_price;
"
"
"
"
if (abs(price_diff) <= epsilon)
"
"
{
"
"
break;
"
"
};
"
"
"
"
var vega := bsm_vega(s, k, r, t, vola);
"
"
"
"
if (vega < epsilon)
"
"
{
"
"
itr := max_iters + 1;
"
"
break;
"
"
};
"
"
"
"
vola -= price_diff / vega;
"
"
};
"
"
"
"
itr <= max_iters ? vola : 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
(
"
bsm_vega
"
)
.
vars
(
"
s
"
,
"
k
"
,
"
r
"
,
"
t
"
,
"
v
"
)
.
expression
(
"
var d1 := (log(s / k) + (r + v^2 / 2) * t) / (v * sqrt(t));
"
"
s * exp(-d1^2 / 2) / sqrt(2pi) * sqrt(t);
"
));
expression_t
expression;
expression.
register_symbol_table
(symbol_table);
parser_t
parser;
parser.
compile
(option_implied_volatility_program, expression);
{
callput_flag =
"
call
"
;
target_price =
T
(
18.339502
);
const
T call_option_implied_vola = 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, call_option_implied_vola);
}
{
callput_flag =
"
put
"
;
target_price =
T
(
16.782764
);
const
T put_option_implied_vola = 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, put_option_implied_vola);
}
}
int
main
()
{
compute_european_option_implied_volatility<
double
>();
return
0
;
}
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