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:
* https://arrayfire.com/licenses/BSD-3-Clause
********************************************************/
#include <arrayfire.h>
#include <math.h>
#include <stdio.h>
#include <cstdlib>
#include <iostream>
#include "input.h"
using namespace af;
// Use the relationship between the cumulative normal distribution and the
// (complementary) error function:
// https://en.wikipedia.org/wiki/Error_function#Cumulative_distribution_function
array cnd(array x) {
const float sqrt05 = sqrt(0.5f);
return 0.5f * erfc(-x * sqrt05);
}
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");
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
for (int i = 0; i < iter; i++) {
black_scholes(Cg, Pg, Sg, Xg, Rg, Vg, Tg);
eval(Cg, Pg);
}
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;
}
af::dim4
Generic object that represents size and shape.
Definition: dim4.hpp:33
af::erfc
AFAPI array erfc(const array &in)
C++ Interface for complementary error function value.
af::exp
AFAPI array exp(const array &in)
C++ Interface for exponential of an array.
af::info
AFAPI void info()
af::setDevice
AFAPI void setDevice(const int device)
Sets the current device.
af::log
AFAPI array log(const array &in)
C++ Interface for natural logarithm.
af::timer::start
static AFAPI timer start()
af::array
A multi dimensional data container.
Definition: array.h:35
af
Definition: algorithm.h:15
af::sqrt
AFAPI array sqrt(const array &in)
C++ Interface for square root of input.
af::exception
An ArrayFire exception class.
Definition: exception.h:29
af::tile
AFAPI array tile(const array &in, const unsigned x, const unsigned y=1, const unsigned z=1, const unsigned w=1)
af::array::dims
dim4 dims() const
Get dimensions of the array.
af::timer::stop
static AFAPI double stop()
arrayfire.h
af::sync
AFAPI void sync(const int device=-1)
Blocks until the device is finished processing.
af::eval
array & eval(array &a)
Evaluate an expression (nonblocking).
Definition: array.h:1354
af::exception::what
virtual const char * what() const
Returns an error message for the exception in a string format.
Definition: exception.h:60