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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

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    1. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    2. Jiao, Ying & Ma, Chunhua & Scotti, Simone & Sgarra, Carlo, 2019. "A branching process approach to power markets," Energy Economics, Elsevier, vol. 79(C), pages 144-156.
    3. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    4. Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR model with branching processes in sovereign interest rate modeling," Finance and Stochastics, Springer, vol. 21(3), pages 789-813, July.
    5. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes," Journal of Finance, American Finance Association, vol. 59(3), pages 1405-1440, June.
    6. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    7. Damir Filipovic, 2001. "A general characterization of one factor affine term structure models," Finance and Stochastics, Springer, vol. 5(3), pages 389-412.
    8. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    9. Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Post-Print hal-01275397, HAL.
    10. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    11. Ying Jiao & Chunhua Ma & Simone Scotti & Chao Zhou, 2021. "The Alpha‐Heston stochastic volatility model," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 943-978, July.
    12. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    13. Ying Jiao & Chunhua Ma & Simone Scotti & Carlo Sgarra, 2019. "A branching process approach to power markets," Post-Print hal-02954986, HAL.
    14. repec:dau:papers:123456789/1392 is not listed on IDEAS
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