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exprtk_bsm_benchmark.cpp
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exprtk_bsm_benchmark.cpp
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/*
**************************************************************
* C++ Mathematical Expression Toolkit Library *
* *
* ExprTk Black Scholes Merton Benchmark *
* Author: Arash Partow (1999-2023) *
* 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 *
* *
**************************************************************
*/
#include <cstdio>
#include <string>
#include "exprtk.hpp"
static const std::size_t rounds = 20000000;
template <typename T>
struct bsm_parameters
{
T s; // Stock price
T x; // Strike price
T t; // Years to maturity
T r; // Risk free rate
T v; // Volatility
};
const bsm_parameters<double> bsm_list[] =
{
{ 60.11, 65.11, 0.25, 0.08, 0.31 },
{ 60.22, 65.22, 0.25, 0.08, 0.32 },
{ 60.33, 65.33, 0.25, 0.08, 0.33 },
{ 60.44, 65.44, 0.25, 0.08, 0.34 },
{ 60.55, 65.55, 0.25, 0.08, 0.35 },
{ 60.66, 65.66, 0.25, 0.08, 0.36 },
{ 60.77, 65.77, 0.25, 0.08, 0.37 },
{ 60.88, 65.88, 0.25, 0.08, 0.38 },
{ 60.11, 65.11, 0.25, 0.08, 0.31 },
{ 60.22, 65.22, 0.25, 0.08, 0.32 },
{ 60.33, 65.33, 0.25, 0.08, 0.33 },
{ 60.44, 65.44, 0.25, 0.08, 0.34 },
{ 60.55, 65.55, 0.25, 0.08, 0.35 },
{ 60.66, 65.66, 0.25, 0.08, 0.36 },
{ 60.77, 65.77, 0.25, 0.08, 0.37 },
{ 60.88, 65.88, 0.25, 0.08, 0.38 }
};
const std::size_t bsm_list_size = sizeof (bsm_list) / sizeof(bsm_parameters<double>);
template <typename T>
void black_scholes_merton_model()
{
typedef exprtk::symbol_table<T> symbol_table_t;
typedef exprtk::expression<T> expression_t;
typedef exprtk::parser<T> parser_t;
const std::string bsm_model_program =
" var d1 := (log(s / x) + (r + v^2 / 2) * t) / (v * sqrt(t)); "
" var d2 := d1 - v * sqrt(t); "
" "
" if (callput_flag == 'call') "
" s * ncdf(d1) - x * e^(-r * t) * ncdf(d2); "
" else if (callput_flag == 'put') "
" x * e^(-r * t) * ncdf(-d2) - s * ncdf(-d1); "
" ";
const std::string bsm_model_program_opt1 =
" var v_sqrtt := (v * sqrt(t)); "
" var d1 := (log(s / x) + (r + v * v / 2) * t) / v_sqrtt; "
" var d2 := d1 - v_sqrtt; "
" var xert := x * exp(-r * t); "
" "
" if (callput_flag == 'call') "
" s * ncdf(d1) - xert * ncdf(d2); "
" else if (callput_flag == 'put') "
" xert * ncdf(-d2) - s * ncdf(-d1); "
" ";
const std::string bsm_model_program_opt2 =
" var v_sqrtt := (v * sqrt(t)); "
" var d1 := (log(s / x) + (r + v * v / 2) * t) / v_sqrtt; "
" var d2 := d1 - v_sqrtt; "
" "
" if (callput_flag == 'call') "
" s * ncdf(d1) - (x * exp(-r * t)) * ncdf(d2); "
" else if (callput_flag == 'put') "
" (x * exp(-r * t)) * ncdf(-d2) - s * ncdf(-d1); "
" ";
T s = T(0);
T x = T(0);
T t = T(0);
T r = T(0);
T v = T(0);
std::string callput_flag;
static const T e = exprtk::details::numeric::constant::e;
symbol_table_t symbol_table;
symbol_table.add_variable("s",s);
symbol_table.add_variable("x",x);
symbol_table.add_variable("t",t);
symbol_table.add_variable("r",r);
symbol_table.add_variable("v",v);
symbol_table.add_constant("e",e);
symbol_table.add_stringvar("callput_flag",callput_flag);
expression_t bsm_expression (symbol_table);
expression_t bsm_expression_opt1(symbol_table);
expression_t bsm_expression_opt2(symbol_table);
parser_t parser;
parser.compile(bsm_model_program , bsm_expression );
parser.compile(bsm_model_program_opt1, bsm_expression_opt1);
parser.compile(bsm_model_program_opt2, bsm_expression_opt2);
{
exprtk::timer timer;
timer.start();
T total = T(0);
for (std::size_t k = 0; k < rounds; ++k)
{
const bsm_parameters<T>& params = bsm_list[k % bsm_list_size];
s = params.s;
x = params.x;
t = params.t;
r = params.r;
v = params.v;
callput_flag = "call";
total += bsm_expression.value();
callput_flag = "put";
total += bsm_expression.value();
}
timer.stop();
printf("[exprtk0] Total: %16.5f\tTime:%8.3fsec\tRate:%16.3f\n",
total,
timer.time(),
(2.0 * rounds) / timer.time());
}
{
exprtk::timer timer;
timer.start();
T total = T(0);
for (std::size_t k = 0; k < rounds; ++k)
{
const bsm_parameters<T>& params = bsm_list[k % bsm_list_size];
s = params.s;
x = params.x;
t = params.t;
r = params.r;
v = params.v;
callput_flag = "call";
total += bsm_expression_opt1.value();
callput_flag = "put";
total += bsm_expression_opt1.value();
}
timer.stop();
printf("[exprtk1] Total: %16.5f\tTime:%8.3fsec\tRate:%16.3f\n",
total,
timer.time(),
(2.0 * rounds) / timer.time());
}
{
exprtk::timer timer;
timer.start();
T total = T(0);
for (std::size_t k = 0; k < rounds; ++k)
{
const bsm_parameters<T>& params = bsm_list[k % bsm_list_size];
s = params.s;
x = params.x;
t = params.t;
r = params.r;
v = params.v;
callput_flag = "call";
total += bsm_expression_opt2.value();
callput_flag = "put";
total += bsm_expression_opt2.value();
}
timer.stop();
printf("[exprtk2] Total: %16.5f\tTime:%8.3fsec\tRate:%16.3f\n",
total,
timer.time(),
(2.0 * rounds) / timer.time());
}
}
template <typename T>
inline T bsm_model(const std::string& callput_flag, const T s, const T x, const T t, const T r, const T v)
{
const T d1 = (std::log(s / x) + (r + (v * v) / 2) * t) / (v * std::sqrt(t));
const T d2 = d1 - v * sqrt(t);
if (callput_flag == "call")
return s * exprtk::details::numeric::ncdf(d1) - x * exp(-r * t) * exprtk::details::numeric::ncdf(d2);
else if (callput_flag == "put")
return x * exp(-r * t) * exprtk::details::numeric::ncdf(-d2) - s * exprtk::details::numeric::ncdf(-d1);
else
return T(0);
}
template <typename T>
void bsm_native()
{
T s = T(0);
T x = T(0);
T t = T(0);
T r = T(0);
T v = T(0);
std::string callput_flag;
exprtk::timer timer;
timer.start();
T total = T(0);
for (std::size_t k = 0; k < rounds; ++k)
{
const bsm_parameters<T>& params = bsm_list[k % bsm_list_size];
s = params.s;
x = params.x;
t = params.t;
r = params.r;
v = params.v;
callput_flag = "call";
total += bsm_model(callput_flag, s, x, t, r, v);
callput_flag = "put";
total += bsm_model(callput_flag, s, x, t, r, v);
}
timer.stop();
printf("[native ] Total: %16.5f\tTime:%8.3fsec\tRate:%16.3f\n",
total,
timer.time(),
(2.0 * rounds) / timer.time());
}
int main()
{
black_scholes_merton_model<double>();
bsm_native<double>();
return 0;
}
/*
Build command:
c++ -pedantic-errors -Wall -Wextra -Werror -Wno-long-long -flto -march=native -O3 -o exprtk_bsm_benchmark exprtk_bsm_benchmark.cpp -L/usr/lib -lstdc++ -lm
*/