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arXiv · 2205.12355

CBI-time-changed L\'evy processes

Claudio Fontana·Alessandro Gnoatto·Guillaume Szulda
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Abstract

We introduce and study the class of CBI-time-changed L\'evy processes (CBITCL), obtained by time-changing a L\'evy 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.

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Claudio Fontana, Alessandro Gnoatto, Guillaume Szulda. 2022-05-24. CBI-time-changed L\'evy processes. https://doi.org/10.1016/j.spa.2023.06.005

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