Fluctuation in option pricing using cellular automata based market models

A new agent-based Cellular Automaton (CA) computational algorithm for option pricing is proposed. CAs have been extensively used in modeling complex dynamical systems but not in modeling option prices. Compared with traditional tools, which rely on guessing volatilities to calculate option prices, the CA model is directly addressing market mechanisms and simulates price fluctuation from aggregation of actions made by interacting individual market makers in a large population. This paper explores whether CA models can provide reasonable good answers to pricing European options. The Black-Scholes model and the Binomial Tree model are used for comparison. Comparison reveals that CA models perform reasonably well in pricing options, reproducing overall characteristics of random walk based model, while at the same time providing plausible results for the 'fat-tail' phenomenon observed in many markets. We also show that the binomial tree model can be obtained from a CA rule. Thus, CA models are suitable tools to generalize the standard theories of option pricing.