The Multinomial Option Pricing Model and Its Brownian and Poisson Limits

Abstract

The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths for a wide variety of complete market structures. In the discontinuous case of Merton-type formula is shown to result, provided jump probabilities are replaced by their corresponding Arrow-Debreu prices.