Multi-purpose binomial model: Fitting all moments to the underlying geometric Brownian motion

- We provides a multi-purpose binomial tree model.
- Our model generalizes the Cox-Ross-Rubinstein, Jarrow-Rudd, and Tian models.
- Our model can fit all moments of the approximate geometric Brownian motion.
- Our binomial model is used to resolve the discontinuity problem in option pricing.

We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model is used to resolve a discontinuity problem in option pricing.