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Dependent Default Modeling through Multivariate Generalized Cox Processes

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  • Djibril Gueye
  • Alejandra Quintos

Abstract

We propose a multivariate framework for modeling dependent default times that extends the classical Cox process by incorporating both common and idiosyncratic shocks. Our construction uses c\`adl\`ag, increasing processes to model cumulative intensities, relaxing the requirement of absolutely continuous compensators. Analytical tractability is preserved through the multiplicative decomposition of Az\'ema supermartingales under assumptions that guarantee deterministic compensators. The framework captures a wide range of dependence structures and allows for both simultaneous and non-simultaneous defaults. We derive closed-form expressions for joint survival probabilities and illustrate the flexibility of the model through examples based on L\'evy subordinators, compound Poisson processes, and shot-noise processes, encompassing several well-known models from the literature as special cases. Finally, we show how the framework can be extended to incorporate stochastic continuous components, thereby unifying gradual and abrupt sources of default risk.

Suggested Citation

  • Djibril Gueye & Alejandra Quintos, 2025. "Dependent Default Modeling through Multivariate Generalized Cox Processes," Papers 2508.05022, arXiv.org.
    • Handle: RePEc:arx:papers:2508.05022
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    References listed on IDEAS

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    1. Hyunju Lee & Ji Hwan Cha, 2018. "A dynamic bivariate common shock model with cumulative effect and its actuarial application," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(10), pages 890-906, November.
    2. Jan-Frederik Mai & Matthias Scherer, 2009. "A Tractable Multivariate Default Model Based On A Stochastic Time-Change," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 227-249.
    3. Ruixuan Liu, 2020. "A competing risks model with time‐varying heterogeneity and simultaneous failure," Quantitative Economics, Econometric Society, vol. 11(2), pages 535-577, May.
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    Cited by:

    1. Alessio Lapolla, 2025. "A recursive formula for the $n^\text{th}$ survival function and the $n^\text{th}$ first passage time distribution for jump and diffusion processes. Applications to the pricing of $n^\text{th}$-to-defa," Papers 2509.02347, arXiv.org, revised Sep 2025.

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