CBI-time-changed Lévy processes

Claudio Fontana, Alessandro Gnoatto and Guillaume Szulda

Stochastic Processes and their Applications, 2023, vol. 163, issue C, 323-349

Abstract: We introduce and study the class of 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)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:163:y:2023:i:c:p:323-349

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DOI: 10.1016/j.spa.2023.06.005

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