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Density approach in modelling successive defaults

Author

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  • Nicole El Karoui

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Monique Jeanblanc

    (LAP - Laboratoire Analyse et Probabilités - UEVE - Université d'Évry-Val-d'Essonne)

  • Ying Jiao

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

We apply the default density framework developed in El Karoui et al. \cite{ejj1} to modelling of multiple defaults, which can be adapted to both top-down and bottom-up models. We present general pricing results and establish links with the classical intensity approach. Explicit models are also proposed by using the methods of change of probability measure or dynamic copula.

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  • Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2015. "Density approach in modelling successive defaults," Post-Print hal-00870492, HAL.
    • Handle: RePEc:hal:journl:hal-00870492
    Note: View the original document on HAL open archive server: https://hal.science/hal-00870492
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    References listed on IDEAS

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    1. Alexander Herbertsson, 2011. "Modelling default contagion using multivariate phase-type distributions," Review of Derivatives Research, Springer, vol. 14(1), pages 1-36, April.
    2. Rama Cont & Andreea Minca, 2013. "Recovering portfolio default intensities implied by CDO quotes," Post-Print hal-00413730, HAL.
    3. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2010. "What happens after a default: The conditional density approach," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1011-1032, July.
    4. Kay Giesecke & Lisa R. Goldberg & Xiaowei Ding, 2011. "A Top-Down Approach to Multiname Credit," Operations Research, INFORMS, vol. 59(2), pages 283-300, April.
    5. Frey, Rüdiger & Backhaus, Jochen, 2010. "Dynamic hedging of synthetic CDO tranches with spread risk and default contagion," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 710-724, April.
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    Cited by:

    1. Biagini, Francesca & Mazzon, Andrea & Oberpriller, Katharina, 2023. "Reduced-form framework for multiple ordered default times under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 1-43.
    2. Ying Jiao & Yahia Salhi & Shihua Wang, 2022. "Dynamic Bivariate Mortality Modelling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 917-938, June.
    3. Fang, Jun & Jiang, Fan & Liu, Yong & Yang, Jingping, 2020. "Copula-based Markov process," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 166-187.
    4. Ying Jiao & Yahia Salhi & Shihua Wang, 2021. "Dynamic Bivariate Mortality Modelling," Working Papers hal-03244324, HAL.
    5. Francesca Biagini & Andrea Mazzon & Katharina Oberpriller, 2021. "Reduced-form framework for multiple ordered default times under model uncertainty," Papers 2108.04047, arXiv.org, revised Oct 2022.

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