A GENERAL SUBORDINATED STOCHASTIC PROCESS FOR DERIVATIVES PRICING

A general subordinated stochastic process is proposed to model the dynamics of the underlying asset of an option. We prove that this class of models can be considered generically as the limit of discrete time models in which the number of transactions is random. We also derive several results for the valuation of contingent claims in this framework. In particular, we compare the impacts of different choices of subordinator processes on the option valuation.