The Multinomial Option Pricing Model and Its Brownian and Poisson Limits - Madan, Dilip B.; Milne, Frank; Shefrin, Hersh (Review of Financial Studies, 1989)
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.