August 2009
Intermediate to advanced
244 pages
9h 5m
English
Content preview from Financial Modelling in Python
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9
Pricing using Numerical Methods
As the demand for ever more complex financial structures grows and the trend towards
multi-asset products accelerates, quantitative analysts will resort more and more to numerical
methods to solve their pricing problems. The two most common approaches currently in use
are Monte-Carlo simulation and lattice integration schemes, for example finite difference. In
this chapter we will develop a general framework for both approaches that can be used to price
a large set of pricing problems. The ultimate goal of the chapter is to arrive at a design where
the pricing frameworks are invariant over the pricing model used.
9.1 A LATTICE PRICING FRAMEWORK
Let us begin this section by outlining the domain of problems the lattice pricing framework to
be developed will be able to handle. Firstly, the pricing model needs to be a low-dimensional
Markovian model otherwise the time taken to price becomes prohibitive; and, secondly, the
financial instrument must not be path-dependent. If these two criteria are satisfied, then
the following framework is applicable. The second criterion can be relaxed, through the
introduction of state-variables, to include only strongly path-dependent instruments. However
this next step is beyond the scope of the book and we leave it as an exercise for the reader.
The aforementioned
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