Financial Modelling in Python

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c04 JWBK378-Fletcher May 23, 2009 4:21 Printer: Yet to come

28 Financial Modelling in Python

for o, a in opts:

if o in ("-h", "--help"):

help()

sys.exit()

if o in ("-v", "--version"):

print "‘%s’, Version 0.0.0" % sys.argv[0]

sys.exit()

print gauss()

print lognormal variate()

4.2 N(.)

In the ppf.math.special functions module, N is a function that approximates the

standard normal cumulative distribution function, N(.), as used in the celebrated Black–Scholes

option-pricing equation.

import math

def N(x):

a = 0.3535533905933

b1 = -1.2655122300000

b2 = 1.0000236800000

b3 = 0.3740919600000

b4 = 0.0967841800000

b5 = -0.1862880600000

b6 = 0.2788680700000

b7 = -1.1352039800000

b8 = 1.4885158700000

b9 = -0.8221522300000

b10 = 0.1708727700000

t, term, result = 0, 0, 0

if(x > 0):

if (x > 10): result = 1.0

else:

t = 1/(1 + a*x)

term = b9 + t*b10

term = b8 + t*term

term = b7 + t*term

term = b6 + t*term

term = b5 + t*term

term = b4 + t*term

term = b3 + t*term

term = b2 + t*term

term = b1 + t*term

term = term + -0.5*(x*x)

result = 1.0 - 0.5*t*math.exp(term)

else: