We will investigate the relation between Bachelier and Black-Scholes models driven by the infinitely divisible inverse subordinators. Such models, in contrast to their classical equivalents, can be used in markets where periods of stagnation are observed. We will introduce the subordinated Cox-Ross-Rubinstein model and prove that the price of the underlying in that model converges in distribution and in Skorokhod space to the price of underlying in the subordinated Black-Scholes model. Motivated by this fact we will price the selected option contracts using the binomial trees. The comparison to other numerical methods will be provided.