Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2012.1978.1981GanikhodjaevNasirBayramKamola1220121218In 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 (U_{n}, D_{n}),
where {U_{n}} and {D_{n}} be the sequences of independent, identically
distributed random variables with U_{n}>1 and 0<D_{n}<1<U_{n}
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.]]>Cox, J.C., S.A. Ross and M. Rubinstein,1979Rendleman Jr., R.J. and B.J. Bartter,1979Hull, J.C.,2011Pascucci, A.,2011Black, F. and M. Scholes,1973Georgiadis, E.,2011Merton, R.C.,1973Solomon, F.,1975Menshikov, M. and D. Peteritis,2001