financial/black_scholes_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:
* http://arrayfire.com/licenses/BSD-3-Clause
********************************************************/
#include <iostream>
#include <stdio.h>
#include <math.h>
#include <arrayfire.h>
#include <cstdlib>
#include "input.h"
using namespace af;
// The following function is a modified version of http://www.johndcook.com/blog/cpp_phi/
// The example above references Handbook of Mathematical Functions by Abramowitz and Stegun
array cnd(array x)
{
// constants
const float a1 = 0.254829592;
const float a2 = -0.284496736;
const float a3 = 1.421413741;
const float a4 = -1.453152027;
const float a5 = 1.061405429;
const float p = 0.3275911;
const float sqrt2 = sqrt(2.0);
// Save the sign of x
array xSign = sign(x);
x = abs(x) / sqrt2;
// A&S formula 7.1.26
array t = 1.0f / (1.0f + p*x);
array y = 1.0f + 0.5f * (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*exp(-x*x);
return xSign * y + !xSign * (1 - y); // equivalent of (x >= 0) ? y : (1 - y);
}
static void black_scholes(array& C, array& P,
const array& S, const array& X,
const array& R, const array& V,
const array& T)
{
// This function computes the call and put option prices based on
// Black-Scholes Model
// S = Underlying stock price
// X = Strike Price
// R = Risk free rate of interest
// V = Volatility
// T = Time to maturity
array d1 = log(S / X);
d1 = d1 + (R + (V*V)*0.5) * T;
d1 = d1 / (V*sqrt(T));
array d2 = d1 - (V*sqrt(T));
array cnd_d1 = cnd(d1);
array cnd_d2 = cnd(d2);
C = S * cnd_d1 - (X * exp((-R)*T) * cnd_d2);
P = X * exp((-R)*T) * (1 - cnd_d2) - (S * (1 - cnd_d1));
}
int main(int argc, char **argv)
{
try {
int device = argc > 1 ? atoi(argv[1]) : 0;
setDevice(device);
info();
printf("** ArrayFire Black-Scholes Example **\n"
"** by AccelerEyes **\n\n");
array GC1(4000, 1, C1);
array GC2(4000, 1, C2);
array GC3(4000, 1, C3);
array GC4(4000, 1, C4);
array GC5(4000, 1, C5);
// Compile kernels
// Create GPU copies of the data
array Sg = GC1;
array Xg = GC2;
array Rg = GC3;
array Vg = GC4;
array Tg = GC5;
array Cg, Pg;
// Warm up black scholes example
black_scholes(Cg, Pg, Sg,Xg,Rg,Vg,Tg);
eval(Cg, Pg);
printf("Warming up done\n");
af::sync();
int iter = 1000;
for (int n = 50; n <= 500; n += 50) {
// Create GPU copies of the data
Sg = tile(GC1, n, 1);
Xg = tile(GC2, n, 1);
Rg = tile(GC3, n, 1);
Vg = tile(GC4, n, 1);
Tg = tile(GC5, n, 1);
af::eval(Sg, Xg, Rg, Vg, Tg);
dim4 dims = Xg. dims();
// Force compute on the GPU
af::sync();
timer::start();
for (int i = 0; i < iter; i++) {
black_scholes(Cg, Pg, Sg,Xg,Rg,Vg,Tg);
eval(Cg, Pg);
}
af::sync();
double t = timer::stop() / iter;
printf("Input Data Size = %8d. Mean GPU Time: %0.6f ms\n", (int)dims[0], 1000 * t);
}
} catch (af::exception& e){
fprintf(stderr, "%s\n", e. what());
throw;
}
return 0;
}