Financial Modelling in Python

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Basic Mathematical Tools 29

if(x < -10): result = 0.0

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 = 0.5*t*math.exp(term)

return result

4.3 INTERPOLATION

Interpolation is the process of estimating the values of a function y(x) for arguments between

x

0

, ..., x

n

at which the values y

0

, ..., y

n

are known. To elegantly implement interpolation

schemes in a single dimension, it is helpful to first define some utility functions for searching

an ordered sequence of numbers. The ppf.utility.bound module defines a family of

such functions in the spirit of the C++ STL

2

functions of the same names.

import operator

def lower

bound(x, values, cmp=operator.lt):

"""Find the first position in values

where x could be inserted without violating

the ordering.

"""

first, count = 0, len(values)

while count > 0:

half = count/2

middle = first + half

if cmp(values[middle], x):

first = middle + 1

count = count - half - 1

else: count = half

return first

def upper

bound(x, values, cmp=operator.lt):

"""Find the last position in values

where x could be inserted without changing

the ordering.

2

The C++ STL (Standard Template Library) is a generic library of class templates and algorithms.

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