blackscholes.py

from __future__ import print_function

import time

import numpy as np

RISKFREE = 0.02
VOLATILITY = 0.30


def cnd(d):
    A1 = 0.31938153
    A2 = -0.356563782
    A3 = 1.781477937
    A4 = -1.821255978
    A5 = 1.330274429
    RSQRT2PI = 0.39894228040143267793994605993438
    K = 1.0 / (1.0 + 0.2316419 * np.abs(d))
    ret_val = (RSQRT2PI * np.exp(-0.5 * d * d) *
               (K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5))))))
    return np.where(d > 0, 1.0 - ret_val, ret_val)

    # Despite the memory overhead and redundant computation, the above
    # is much faster than:

    # for i in range(len(d)):
    #     if d[i] > 0:
    #         ret_val[i] = 1.0 - ret_val[i]
    # return ret_val


def black_scholes(callResult, putResult, stockPrice, optionStrike, optionYears,
                  Riskfree, Volatility):
    S = stockPrice
    X = optionStrike
    T = optionYears
    R = Riskfree
    V = Volatility
    sqrtT = np.sqrt(T)
    d1 = (np.log(S / X) + (R + 0.5 * V * V) * T) / (V * sqrtT)
    d2 = d1 - V * sqrtT
    cndd1 = cnd(d1)
    cndd2 = cnd(d2)

    expRT = np.exp(- R * T)
    callResult[:] = (S * cndd1 - X * expRT * cndd2)
    putResult[:] = (X * expRT * (1.0 - cndd2) - S * (1.0 - cndd1))


def randfloat(rand_var, low, high):
    return (1.0 - rand_var) * low + rand_var * high


def main (*args):
    OPT_N = 4000000
    iterations = 10
    if len(args) >= 2:
        iterations = int(args[0])

    callResult = np.zeros(OPT_N)
    putResult = -np.ones(OPT_N)
    stockPrice = randfloat(np.random.random(OPT_N), 5.0, 30.0)
    optionStrike = randfloat(np.random.random(OPT_N), 1.0, 100.0)
    optionYears = randfloat(np.random.random(OPT_N), 0.25, 10.0)

    time0 = time.time()
    for i in range(iterations):
        black_scholes(callResult, putResult, stockPrice, optionStrike,
                      optionYears, RISKFREE, VOLATILITY)
    time1 = time.time()
    print("Time: %f msec" % ((time1 - time0) / iterations * 1000))


if __name__ == "__main__":
    import sys
    main(*sys.argv[1:])