The famous Black–Sholes (BS) and Cox–Ross–Rubinstein (CRR) formulas are basic results in the modern theory of option pricing in financial mathematics. They are usually deduced by means of stochastic analysis; various generalisations of these formulas were proposed using more sophisticated stochastic models for common stocks pricing evolution. In this paper we develop systematically a deterministic approach to the option pricing that leads to a different type of generalisations of BS and CRR formulas...