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This paper develops a stochastic volatility model, which overcomes the Black-Scholes model tendency to overprice near at-the-money options and underprice deep out Or in-the-money options. In contrast to the previous literature that assumes diffusion volatilities, this paper assumes that the volatility follows a Markov chain on a discrete state space. This intuitive approach has easier mathematics and, by taking limit, the diffusion results can be obtained. By generalizing the binomial model to the Markovian volatility model, a refursive pricing scheme is first developed, under a particular assumption on prefer.ence to the volatility dynamics, and then a continuous time result by taking limit. The both discrete and continuous models give general conditions under which the call value is increasing in the current volatility. Also. based on the local convexity and concavity of thp Black-Scholes equation in volatility, we explain why the deficits of the Black-Scholes equation take place. Some numerical experiments are also given to support our results.

A SIMPLE OPTION PRICING MODEL WITH MARKOVIAN VOLATILITIES