Financial Modelling in Python

P1: JYS

c05 JWBK378-Fletcher May 12, 2009 16:54 Printer: Yet to come

5

Market: Curves and Surfaces

A financial market is made up out of lots of pieces of information. For example, foreign

exchange rates, equity spot prices, yield curves, volatility surfaces and correlation surfaces,

to name a few. In this chapter we discuss simple classes for representing curves and surfaces

provided in the ppf.market subpackage. The chapter is concluded with a discussion of the

market environment which is designed to represent a financial market.

5.1 CURVES

Fundamentally, without regard to the specific market variable being modelled (e.g. discount

factors, forward rates, volatilities at a fixed strike and expiry for a range of tenors), a curve is

the association between a set of points at which the function is known (abscissae), the known

function values at those points (ordinates) and an interpolation algorithm for estimating the

value of the function between the known abscissae. Utilisation of the interpolation algorithms

presented in section 4.3 deals with the ‘heavy lifting’ of curve representation. From the

ppf.market.curve module we have the simple curve

class curve:

def

init (self, times, factors, interp):

self.

impl = interp(times, factors)

def

call (self, t): return self. impl(t)

The following interpreter transcript (simulating a discount factor curve) shows how easily

a curve can be modelled by these components: ...