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.
- Cox-Ross-Rubinstein binomial model
- Itô price process
- Poisson process
- geometric Brownian motion
- trinomial model