Random Binomial Tree Models and Options

In this study, we introduce the simplest random binomial tree model. Usual binomial tree model is prescribed by pair of numbers (u, d), where u denotes the increase rate of the stock over the fixed period of time and d denotes the decrease rate, with 0n, Dn), where {Un} and {Dn} be the sequences of independent, identically distributed random variables with Un>1 and 0n<1n for all n, is called a random environment and binomial tree model with random environment is called random binomial tree model. In this paper, we define and study European call option for such models.