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Time-changed CIR default intensities with two-sided mean-reverting jumps

Author

Listed:
  • Rafael Mendoza-Arriaga
  • Vadim Linetsky
Abstract
The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process $(X,D)$ of a diffusion state variable $X$ driving default intensity and a default indicator process $D$ and time change it with a L\'{e}vy subordinator ${\mathcal{T}}$. We characterize the time-changed process $(X^{\phi}_t,D^{\phi}_t)=(X({\mathcal{T}}_t),D({\mathcal{T}}_t))$ as a Markovian--It\^{o} semimartingale and show from the Doob--Meyer decomposition of $D^{\phi}$ that the default time in the time-changed model has a jump-diffusion or a pure jump intensity. When $X$ is a CIR diffusion with mean-reverting drift, the default intensity of the subordinate model (SubCIR) is a jump-diffusion or a pure jump process with mean-reverting jumps in both directions that stays nonnegative. The SubCIR default intensity model is analytically tractable by means of explicitly computed eigenfunction expansions of relevant semigroups, yielding closed-form pricing of credit-sensitive securities.

Suggested Citation

  • Rafael Mendoza-Arriaga & Vadim Linetsky, 2014. "Time-changed CIR default intensities with two-sided mean-reverting jumps," Papers 1403.5402, arXiv.org.
    • Handle: RePEc:arx:papers:1403.5402
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    References listed on IDEAS

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    Cited by:

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    3. Yan Qu & Angelos Dassios & Hongbiao Zhao, 2023. "Shot-noise cojumps: Exact simulation and option pricing," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 74(3), pages 647-665, March.
    4. Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
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    6. Frédéric Vrins, 2017. "Wrong-Way Risk Cva Models With Analytical Epe Profiles Under Gaussian Exposure Dynamics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-35, November.
    7. Pingping Jiang & Bo Li & Yongjin Wang, 2020. "Exit Times, Undershoots and Overshoots for Reflected CIR Process with Two-Sided Jumps," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 693-710, June.
    8. Cheikh Mbaye & Frédéric Vrins, 2018. "A Subordinated Cir Intensity Model With Application To Wrong-Way Risk Cva," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-22, November.
    9. Cheikh Mbaye & Frédéric Vrins, 2022. "Affine term structure models: A time‐change approach with perfect fit to market curves," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 678-724, April.
    10. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    11. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2021. "Random variate generation for exponential and gamma tilted stable distributions," LSE Research Online Documents on Economics 108593, London School of Economics and Political Science, LSE Library.
    12. Michael B. Gordy & Pawel J. Szerszen, 2015. "Bayesian Estimation of Time-Changed Default Intensity Models," Finance and Economics Discussion Series 2015-2, Board of Governors of the Federal Reserve System (U.S.).
    13. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2023. "Shot-noise cojumps: exact simulation and option pricing," LSE Research Online Documents on Economics 111537, London School of Economics and Political Science, LSE Library.
    14. Mesias Alfeus & Kirsty Fitzhenry & Alessia Lederer, 2024. "Stochastic Default Risk Estimation Evidence from the South African Financial Market," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1715-1756, September.
    15. Jang, Jiwook & Mohd Ramli, Siti Norafidah, 2015. "Jump diffusion transition intensities in life insurance and disability annuity," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 440-451.

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