  In this paper, we 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 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 defined in [31]. Motivated
by this fact we price the selected option contracts using the binomial trees.
The results are compared to other numerical methods.
