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CBI-time-changed Lévy processes

Author

Listed:
  • Claudio Fontana

    (Department of Mathematics “Tullio Levi Civita”, University of Padova)

  • Alessandro Gnoatto

    (Department of Economics (University of Verona))

  • Guillaume Szulda

    (Laboratoire de Probabilités, Statistique et Mode ́lisation (LPSM), Paris Diderot University)

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.

Suggested Citation

  • Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2022. "CBI-time-changed Lévy processes," Working Papers 05/2022, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:05/2022
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    References listed on IDEAS

    as
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