Markov Tree Options Pricing

Abstract

This paper questions one of the fundamental assumptions made in options pricing: that the daily returns of a stock are independent and identically distributed (IID). We apply an estimation procedure to years of daily return data for all stocks in the French CAC-40 index. We find six stocks whose log returns are best modeled by a first-order Markov chain, not an IID sequence. We further propose the Markov tree (MT) model, a modification of the standard binomial options pricing model, that takes into account this first-order Markov behavior. Empirical tests reveal that, for the six stocks found earlier, the MT model’s option prices agree very closely with market prices.