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CBI-time-changed Lévy processes

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  • Fontana, Claudio
  • Gnoatto, Alessandro
  • Szulda, Guillaume

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.

Suggested Citation

  • Fontana, Claudio & Gnoatto, Alessandro & Szulda, Guillaume, 2023. "CBI-time-changed Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 323-349.
    • Handle: RePEc:eee:spapps:v:163:y:2023:i:c:p:323-349
    DOI: 10.1016/j.spa.2023.06.005
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