Binomial Trees : Option Pricing Model And The Black Scholes Model

909 Words Jun 7th, 2016 4 Pages
In finance literatures, the most prevail two methods are the Binomial Trees
Option Pricing Model and the Black-Scholes Model. The Binomial Trees Model
(the CRR binomial trees), proposed by Cox, Ross, and Rubinstein in 1979, is a discrete model which has been proved that it converges to the Black-Scholes formula when time increments approach to zero[12]. Because of its flexibility and the ease of computation, it can be used to price the European option as well as American option, while the Black-Scholes Model is not pritical in valuation of early exercised options, like American option, for it tends to exhibit systematic empirical biases related to the exercise price, the time to maturity and the variance when used in pricing the American option [? ].
However, both these two methods are under the assumption that investors well know about the underlying asset, for instance in Black-Scholes model the stock movements are assumed to follow the lognormal distribution. Besides, for these models, the market is complete without any arbitrage opportunity. All these assumptions conflict to the real world. From this perspective, undoubtedly, implementing Nonparametric
Predictive Inference (NPI) method in the option pricing procedure is reasonable. Since unlike classic method, the CRR binomial trees, the probability of stock up or down movement is constant and precise, the NPI probabilities are in the form of
3
1.1. Imprecise Probability 4 an interval with upper and lower bounds, gained…

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