The observed returns distributions of financial assets are central elements in the pricing of securities like an option that gives its owner the right to trade in a fixed number of shares of a specified common stock at a fixed price at any time on or before a given date. On the one hand, models of capital market equilibrium study the structure of asset prices and its connection with empirical anomalies. On the other hand, option pricing models show empirical biases as the strike price bias or the small effect.

Option pricing theory has a long and illustrious history, but it also underwent a revolutionary change in 1973.  At that time, F.Black and M.Scholes presented the first completely satisfactory equilibrium option pricing model. Afterwards,  in 1979 J.C.Cox, J.E.Ross and M.Rubinstein proposed the new idea  of looking at a binomial pricing model as a discrete-time approximation to continuous-time diffusion and in 1994 S.T.Rachev and L.Rüschendorf  extended the conception by introducing two additional randomizations in the binomial price models seeking more general and more realistic limiting models.

In this paper we expand the Rachev-Rüschendorf asset-pricing model introducing a coupled continuous-time-random-walk (CTRW)-like form for the random number of price changes. Such a form results here from the idea of random coarse graining procedure that resembles the coarse-graining methods of statistical physics, and on the other hand, it can indicate application of CTRW processes, widely used in physics to model anomalous diffusion, to the financial markets. In the framework of the proposed model we derive the limiting distributions of log-returns and the corresponding pricing formulas for European  call option. In order to illustrate the obtained theoretical results we present their applications in description of the real financial data.

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