CBI-time-changed Lévy processes

Claudio Fontana (), Alessandro Gnoatto and Guillaume Szulda ()
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Claudio Fontana: Department of Mathematics “Tullio Levi Civita”, University of Padova
Guillaume Szulda: Laboratoire de Probabilités, Statistique et Mode ́lisation (LPSM), Paris Diderot University

No 05/2022, Working Papers from University of Verona, Department of Economics

Abstract: We introduce and study the class of {em CBI-time-changed Lévy processes} (CBITCL), obtained by time-changing a Lévy process with respect to an integrated continuous-state branching process with immigration (CBI). We characterize CBITCL processes as solutions to a certain stochastic integral equation and relate them to affine stochastic volatility processes. We provide a complete analysis of the time of explosion of exponential moments of CBITCL processes and study their asymptotic behavior. In addition, we show that CBITCL processes are stable with respect to a suitable class of equivalent changes of measure. As illustrated by some examples, CBITCL processes are flexible and tractable processes with a significant potential for applications in finance.

Keywords: Branching process; change of time; affine process; stochastic volatility; moment explosion (search for similar items in EconPapers)
Pages: 24
Date: 2022-05
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