Occupation times of Lévy processes

Abstract

In this paper, we give a complete and succinct proof that an explicit formula for the occupation time holds for all Lévy processes, which is important to the pricing problems of various occupation-time-related derivatives such as step options and corridor options. We construct a sequence of Lévy processes converging to a given Lévy process to obtain our conclusion. Besides financial applications, the mathematical results about occupation times of a Lévy process are of interest in applied probability.