Duality and Derivative Pricing with Time-Changed Lévy Processes

In this paper we study the pricing problem of derivatives written in terms of a two dimensional Time-changed Lévy processes. Then, we examine an existing relation between prices of put and call options, of both the European and the American type. This relation is called put-call duality. It includes as a particular case, the relation known as put-call symmetry. Necessary and sufficient conditions for put-call symmetry to hold are shown, in terms of the triplet of local characteristic of the Time-changed Lévy process. In this way we extend the results obtained by Fajardo and Mordecki (2004a) and Fajardo and Mordecki (2004b) to the case of Time-changed Lévy processes.