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bs_erf_dask.py
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bs_erf_dask.py
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# Copyright (c) 2017, Intel Corporation
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# * Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
# * Neither the name of Intel Corporation nor the names of its contributors
# may be used to endorse or promote products derived from this software
# without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
import base_bs_erf
import dask.array as da
from dask.array import log, sqrt, exp
from base_bs_erf import erf, invsqrt
def black_scholes ( nopt, price, strike, t, rate, vol, schd=None):
mr = -rate
sig_sig_two = vol * vol * 2
P = price
S = strike
T = t
a = log(P / S)
b = T * mr
z = T * sig_sig_two
c = 0.25 * z
y = da.map_blocks(invsqrt, z)
w1 = (a - b + c) * y
w2 = (a - b - c) * y
d1 = 0.5 + 0.5 * da.map_blocks(erf, w1)
d2 = 0.5 + 0.5 * da.map_blocks(erf, w2)
Se = exp(b) * S
call = P * d1 - Se * d2
put = call - P + Se
return da.compute( da.stack((put, call)), get=schd )
base_bs_erf.run("Dask", black_scholes, dask=True)