Financial Modelling in Python

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

4

Basic Mathematical Tools

There are some basic mathematical tools and algorithms that are used constantly in computa-

tional quantitative analysis. Reviewing the implementation of these in Python gives us a good

workout in Python programming and the implementations provide us with needed tools to

construct more advanced programs in later chapters.

4.1 RANDOM NUMBER GENERATION

A module for pseudo-random number generators is provided in the Python libraries. It uses the

Mersenne Twister

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algorithm as the core generator, one of the most extensively tested random

number generation schemes of all time. The following is a program demonstrating how the

module can be used. The program prints, firstly, 100 samples from a Gaussian distribution

with mean µ = 0 and standard deviation σ = 1, and then 100 samples from a lognormal

distribution with the same µ and σ .

import random, sys, getopt

def

print gauss():

g = random.Random(1234)

print [g.gauss(mu = 0, sigma = 1) for i in range(100)]

def

print lognormal variate():

g = random.Random(1234)

print [g.lognormvariate(mu = 0, sigma = 1) for i in range(100)]

def

usage():

print "usage: %s" % sys.argv[0]

print "Try ‘python %s -h’ for more information." % sys.argv[0]

def

help():

print "usage: %s" % sys.argv[0]

print "-h (--help) : print this help message and exit"

print "-v (--version) : print the version number ...