On the Relation Between Binomial and Trinomial Option Pricing Models

This paper shows that the binomial option pricing model, suitably parameterized, is a special case of the explicit finite difference method. To prepare for writing the sequel volume of my new book Derivatives: A PowerPlus Picture Book, I recently reviewed the work on trinomial option pricing since Boyle's 1988 JFQA paper. I found myself attracted to the Kamrad and Ritchken (1991) trinomial model because it seemed to be the "natural" generalization of the binomial model described by Cox, Ross and Rubinstein (1979). In that model, as is quite well known, the underlying asset price moves by return x over each period of elapsed time h, where x equals either u or d, while cash earns return r for sure. The resulting corresponding binomial tree is designed to emulate continuoustime risk-neutral geometric Brownian motion with annualized logarithmic mean log(r/d) -- 2 and variance 2 , where r is the annualized riskless return (discrete) and d is the annualized payout return (discre...