Enhancing Binomial and Trinomial Equity Option Pricing Models

We extend the classical Cox-Ross-Rubinstein binomial model in two ways. We first develop a binomial model with time-dependent parameters that equate all moments of the pricing tree increments with the corresponding moments of the increments of the limiting It\^o price process. Second, we introduce a new trinomial model in the natural (historical) world, again fitting all moments of the pricing tree increments to the corresponding geometric Brownian motion. We introduce the risk-neutral trinomial tree and derive a hedging strategy based on an additional perpetual derivative used as a second asset for hedging in any node of the trinomial pricing tree.