About subordinated generalizations of 3 classical models of option pricing

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 to the price of underlying in the subordinated Black-Scholes model defined in [26]. Motivated by this fact we price the selected option contracts using the binomial trees. The results are compared to other numerical methods.