Financial Modelling in Python

P1: JYS

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

54 Financial Modelling in Python

xcurr = root

xmid = 0.5*(xprev+xcurr)

if d+xmid*(c+xmid*(b+xmid*a)) > 0:

bounds.append([xprev, xcurr])

xprev = xcurr

xcurr = xh

xmid = 0.5*(xprev+xcurr)

if d+xmid*(c+xmid*(b+xmid*a)) > 0:

bounds.append([xprev, xcurr])

return bounds

Note that if there are real roots, then we loop through each of the roots and only add a

subinterval if the function at the mid-point is positive. The actual integration then reduces to

a loop over the bounds and is implemented in the method integral

indicator.

class normal distribution:

def integral

indicator(self, cs, indicator, xl, xh, yls = None,

yhs = None):

‘‘‘

>>> mean = 0.05

>>> vol = 0.1

>>> f = normal

distribution(mean, vol)

>>> yls = f.moments(4, -1)

>>> yhs = f.moments(4, 10000)

>>> cs = [0.0,0.0,1.0,1.0]

>>> print f.integral

indicator(cs, cs, -10000, 10000)

0.014125

>>> print cs[2]*(yhs[2]-yls[2])+cs[3]*(yhs[3]-yls[3])

0.014125

‘‘‘

if xl > xh:

raise RuntimeError, \

"lower bound greater than upper bound of integration" \

"domain"

bounds = self.

bounds (indicator, xl, xh)

sum=0

for bound in bounds:

xll = bound[0]

xrr = bound[1]

yll = None

yrr = None

if xll == xl:

yll = yls

if xrr == xh:

yrr = yhs

sum += self.integral(cs, xll, xrr, yll, yrr)

return sum

We will discover later that it is often useful to regrid a piecewise polynomial representation onto

another grid. The regridding algorithm is