Entropy Binomial Tree Model for Option Pricing

We propose a new strategy to determine the parameters of the binomial tree model, which avoids the existing models' drawback of yielding a negative probability distribution p and avoids the restrictive conditions imposed on these models, such as ud = 1. Specifically, by regarding the price states of the underlying asset (stock) in the binomial tree model at the end of the period t = n Delta t as an information system, we establish an entropy optimization model based on the maximum-entropy principle, from which the probability density of the stock price distribution p, and consequently the up ratio, u, and down ratio, d, are derived. This model is not only easy to solve but also has clear economic and physical meaning. In particular, the solution yielded may be applied to various underlying asset price distribution types. Numerical comparisons with the classical binomial tree (CRR) model, the Black-Scholes (B-S) model, the Jarrow and Rudd (JR) model, and the Trigeorgis (TRG) model show that new model produces more reasonable values of p, u and d, and is easier to be used.