Pricing a Multi-Asset American Option in a Parallel Environment by a Finite Element Method Approach

University essay from Uppsala universitet/Matematiska institutionen

Abstract:

There is the need for applying numerical methods to problems that cannot be solved analytically and as the spatial dimension of the problem is increased the need for computational recourses increase exponentially, a phenomenon known as the “curse of dimensionality”. In the Black-Scholes-Merton framework the American option pricing problem has no closed form solution and a numerical procedure has to be employed for solving a PDE. The multi-asset American option introduces challenging computational problems, since for every added asset the dimension of the PDE is increased by one. One way to deal with the curse of dimensionality is threw parallelism. Here the finite element method-of-lines is used for pricing a multi-asset American option dependent on up to four assets in a parallel environment. The problem is also solved with the PSOR method giving a accurate benchmark used for comparison. In finance the put option is one of the most fundamental derivatives since it is basically asset-value insurance and a lot of research is done in the field of quantitative finance on accurate and fast pricing techniques for the multi-dimensional case.

What most experimenters take for granted before they begin

their experiments is infinitely more interesting than any results

to which their experiments lead.”

Norbert Wiener

As soon as an Analytical Engine exists, it will necessarily guide

the future course of the science. Whenever any result is sought

by its aid, the question will then arise – by what course of calculation

can these results be arrived at by the machine in the shortest time?

Charles Babbage

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