  In this paper, we investigate the relation between Bachelier and
Black-Scholes (B-S) 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 (CRR) model and prove that it converges in
distribution to the subordinated B-S model defined in \cite{gajda}. Motivated
by this fact we price the selected option contracts using the binomial trees.
The results are compared to other numerical methods.
