2) to obtain the generalization of Cox-Ross-Rubinstein option price with respect to the alternative model of the stock price process • (3) to obtain the possible limit of generalized Cox-Ross-Rubinstein option priceThe dissertation consists of four chapters, one of which contains numerical results and corresponding graphs. In the first chapter of dissertation we construct the generalized discrete-time model of the underlying stock price process which can be better approximation to the stock price process than classical random walk.Definition 1.1.1 The model of stock price process is called generalizedAt time t = T − m − 1 the unique replicating strategy φ is correspondingly determined.In the second chapter we impose specific assumptions (constrains) on the new model of stock price process and as a result the multinomial Cox-Ross-Rubinstein Theorem 3.5.1. The following convergence is valid for any dyadic t ∈ [0, T ] lim n→∞ ĈT−m = Ĉt = S t Φ(f 1 (S t , T − t)) − Ke −r(T −t) Φ(f 2 (S t , T − t)),(3.5.1