Financial Modelling in Python

P1: JYS

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

Basic Mathematical Tools 59

def rollback(self, t, T, xt, xT, xtT, ftT, yT):

# create cache of moments

self.

create cached moments(xtT, ftT)

return self.

rollback (t, T, xt, xT, xtT, yT, ftT.regrid,

ftT.integral)

def rollback

max(self, t, T, xt, xT, xtT, ftT, yT):

# create cache of moments

self.

create cached moments(xtT, ftT)

return self.

rollback (t, T, xt, xT, xtT, yT, ftT.regrid,

ftT.integral

max)

Note that we precompute the moments in the function create cached moments() prior

to performing the rollback. Doing this improves the efficiency of the algorithm dramatically

because otherwise we keep computing (unnecessarily) the moments nt times. Typically

nt ≈ 41, so you can see why we make such a huge computational saving by precomputing

the moments.

A number of tests have been written for the semi-analytic domain integrator. The tests can

be found in the module ppf.test.test

math with each separate test represented by a

method of the class integrator

tests. The first test checks that we can perform the

conditional expectation of the following classical exponential martingale correctly

5

:

y

T

= exp



σ X

T

−

1

2

σ

2

T



(4.46)

with σ ∈ R

+

. Because we know y

T

is a martingale the following identity must hold.

E[y

T

|F

t

] = exp



σ X

t

−

1

2

σ

2

t



(4.47)

The snippet of code below gives the details of the test just described.

def lognormal martingale test(self):

integrator = ppf.math.semi ...