Random binomial tree models and options - Ganikhodjaev, Nasir; Bayram, Kamola (Asian Network for Scientific Information, 2012)
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 0<d<1<u. We call the pair (u, d) an environment of the binomial tree model. A pair (Un, Dn), where Un and Dn be the sequences of independent, identically distributed random variables with Un>1 and 0<Dn<1<Un 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.