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Rev Fin 1989; 2:251-265
© 1989 the Society for Financial Studies

Article

The multinomial option pricing model and its Brownian and Poisson limits

DB Madan1, F Milne2 and H Shefrin3
1 College of Business and Management, University of Maryland, College Park, MD 20742, USA
2 Australian National University, Australia
3 Santa Clara University, Santa Clara, USA

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.


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