Dr. Harish Bhat (UC Merced)

Title: Markov Tree Option Pricing

Abstract:The Markov Tree (MT) model generalizes the binomial tree by allowing first-order dependence on past outcomes.  We first review an asymptotic argument showing that the distribution of log returns generated by the MT model can be closely approximated by a mixture of normals with three scalar parameters.  Using this distribution, we develop closed-form expressions for the price of a European call option and the corresponding delta hedge.  We then use five years worth of daily option data to compare the MT model's empirical, out-of-sample performance against that of the Black-Scholes model and Heston's stochastic volatility model.  This comparison includes versions of the MT and Black-Scholes models in which volatilities are either dependent or independent of option strike and maturity.  Our findings indicate that, of the models and fitting procedures considered, the MT model yields the most accurate and least risky single-instrument hedges.