About subordinated generalizations of 3 classical models of option pricing

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.