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#!/usr/bin/python
#######################################################
# Copyright (c) 2015, 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
########################################################
import arrayfire as af
from time import time
import math
import sys
def monte_carlo_options(N, K, t, vol, r, strike, steps, use_barrier = True, B = None, ty = af.Dtype.f32):
payoff = af.constant(0, N, 1, dtype = ty)
dt = t / float(steps - 1)
s = af.constant(strike, N, 1, dtype = ty)
randmat = af.randn(N, steps - 1, dtype = ty)
randmat = af.exp((r - (vol * vol * 0.5)) * dt + vol * math.sqrt(dt) * randmat);
S = af.product(af.join(1, s, randmat), 1)
if (use_barrier):
S = S * af.all_true(S < B, 1)
payoff = af.maxof(0, S - K)
return af.mean(payoff) * math.exp(-r * t)
def monte_carlo_simulate(N, use_barrier, num_iter = 10):
steps = 180
stock_price = 100.0
maturity = 0.5
volatility = 0.3
rate = 0.01
strike = 100
barrier = 115.0
start = time()
for i in range(num_iter):
monte_carlo_options(N, stock_price, maturity, volatility, rate, strike, steps,
use_barrier, barrier)
return (time() - start) / num_iter
if __name__ == "__main__":
if (len(sys.argv) > 1):
af.set_device(int(sys.argv[1]))
af.info()
monte_carlo_simulate(1000, use_barrier = False)
monte_carlo_simulate(1000, use_barrier = True )
af.sync()
for n in range(10000, 100001, 10000):
print("Time for %7d paths - vanilla method: %4.3f ms, barrier method: % 4.3f ms\n" %
(n, 1000 * monte_carlo_simulate(n, False, 100), 1000 * monte_carlo_simulate(n, True, 100)))
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