Occupation times of Lévy processes

Lan Wu () and Xiao Zhang
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Lan Wu: Peking University, Beijing, P. R. China
Xiao Zhang: Peking University, Beijing, P. R. China

International Journal of Financial Engineering (IJFE), 2021, vol. 08, issue 03, 1-10

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.

Keywords: Occupation times; Lévy processes; Laplace transform (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S2424786321420032

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