financial/monte_carlo_options.cpp
/*******************************************************
* Copyright (c) 2014, ArrayFire
* All rights reserved.
*
* This file is distributed under 3-clause BSD license.
* The complete license agreement can be obtained at:
* https://arrayfire.com/licenses/BSD-3-Clause
********************************************************/
#include <arrayfire.h>
#include <math.h>
#include <stdio.h>
#include <af/util.h>
#include <iostream>
using namespace af;
template<class ty>
dtype get_dtype();
template<>
dtype get_dtype<float>() {
return f32;
}
template<>
dtype get_dtype<double>() {
return f64;
}
template<class ty, bool use_barrier>
static ty monte_carlo_barrier(int N, ty K, ty t, ty vol, ty r, ty strike,
int steps, ty B) {
dtype pres = get_dtype<ty>();
array payoff = constant(0, N, 1, pres);
ty dt = t / (ty)(steps - 1);
array s = constant(strike, N, 1, pres);
array randmat = randn(N, steps - 1, pres);
randmat = exp((r - (vol * vol * 0.5)) * dt + vol * sqrt(dt) * randmat);
array S = product(join(1, s, randmat), 1);
if (use_barrier) { S = S * allTrue(S < B, 1); }
payoff = max(0.0, S - K);
ty P = mean<ty>(payoff) * exp(-r * t);
return P;
}
template<class ty, bool use_barrier>
double monte_carlo_bench(int N) {
int steps = 180;
ty stock_price = 100.0;
ty maturity = 0.5;
ty volatility = .30;
ty rate = .01;
ty strike = 100;
ty barrier = 115.0;
for (int i = 0; i < 10; i++) {
monte_carlo_barrier<ty, use_barrier>(
N, stock_price, maturity, volatility, rate, strike, steps, barrier);
}
return timer::stop() / 10;
}
int main() {
try {
// Warm up and caching
monte_carlo_bench<float, false>(1000);
monte_carlo_bench<float, true>(1000);
for (int n = 10000; n <= 100000; n += 10000) {
printf(
"Time for %7d paths - "
"vanilla method: %4.3f ms, "
"barrier method: %4.3f ms\n",
n, 1000 * monte_carlo_bench<float, false>(n),
1000 * monte_carlo_bench<float, true>(n));
}
} catch (af::exception &ae) { std::cerr << ae.what() << std::endl; }
return 0;
}