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In this paper, we investigate the relation between Bachelier andBlack-Scholes models driven by the infinitely divisible inverse subordinators.Such models, in contrast to their classical equivalents, can be used in marketswhere periods of stagnation are observed. We introduce the subordinatedCox-Ross-Rubinstein model and prove that the price of the underlying in thatmodel converges in distribution and in Skorokhod space to the price ofunderlying in the subordinated Black-Scholes model defined in [31]. Motivatedby this fact we price the selected option contracts using the binomial trees.The results are compared to other numerical methods.

About subordinated generalizations of 3 classical models of option pricing