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Evaluating Financial Options Using Continuous Cellular Automata

Michael Kelly
Organization: University of Western Sydney

2004 Wolfram Technology Conference
Conference location

Champaign IL

The traditional use of cellular automata (CA) in the study of scientific topics has been to specify simple rules and see whether the resulting CA structures behave like some known real-world structure that the scientist wishes to model. To this end, Stephen Wolfram specified a simple model for financial market price fluctuations in Chapter 8 of A New Kind of Science. While exhibiting the characteristic fractal property of market prices, this model did not allow an analysis of actual financial instruments. The evaluation of such instruments, especially financial derivatives, constitutes the main task of financial “quants” employed by banks and financial institutions. This paper aims to show that the appropriate modification of the continuous CA transformation rules makes it possible to implement efficient code for the evaluation of financial options by modelling the trinomial lattice structures that correspond to the partial differential equations that describe all option behavior. We show that there are a number of possible models using the built in functions NestList, ListCorrelate, and CellularAutomaton that also evaluate options by mimicking the stochastic evolution of underlying stock prices as CA on a trinomial grid.

The presentation notebook uses the BlackScholes.m package by William Shaw.

*Business and Economics
*Mathematics > Discrete Mathematics > Cellular Automata

Options, Cellular Automata
Downloads Download Wolfram CDF Player

BlackScholes.m (4.7 KB) - Supporting package [for Mathematica 5.0]
MKTechConfSlideShow2004.nb (1.4 MB) - Mathematica Notebook