Generalized Cox-Ross-Rubinstein Binomial Models

Abstract

This paper generalizes the seminal Cox-Ross-Rubinstein (CRR) binomial model by adding a stretch parameter. The generalized CRR (GCRR) model allows us to fine-tune (via the stretch parameter) the lattice structure so as to efficiently price a range of options, such as barrier options. Our analysis provides insights into the fine structure of convergence of the general binomial model to the Black-Scholes formula. We also discuss how to improve the rate of convergence or the oscillatory behavior of the GCRR model. The numerical results suggest that the GCRR models with various modifications are efficient for pricing a range of options.