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The Multinomial Option Pricing Model and Its Brownian and Poisson Limits
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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 a Merton-type formula is shown to result, provided jump probabilities are replaced by their corresponding Arrow-Debreu prices.Multinomial, option, pricing, Brownian, Poisson