Enhancing binomial and trinomial equity option pricing models.

Highlights • The classical Cox–Ross–Rubinstein binomial model is extended in two ways. • Show that CRR-model can be extended to a new version with time-dependent parameters. • Develop a new trinomial model in the natural (historical) world. • Derive a hedging strategy for hedging at any node of the trinomial pricing tree. Abstract 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 Itô 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 at any node of the trinomial pricing tree. [ABSTRACT FROM AUTHOR]