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

Enhancing Binomial and Trinomial Equity Option Pricing Models