A dynamic default dependence model
We develop a dynamic multivariate default model for a portfolio of credit-risky assets in which default times are modelled as random variables with possibly different marginal distributions, and Lï¿½vy subordinators are used to model the dependence among default times. In particular, we define a cumulative dynamic hazard process as a Lï¿½vy subordinator, which allows for jumps and induces positive probabilities of joint defaults. We allow the main asset classes in the portfolio to have different cumulative default probabilities and corresponding different cumulative hazard processes. Under this heterogeneous assumption we compute the portfolio loss distribution in closed form. Using an approximation of the loss distribution, we calibrate the model to the tranches of the iTraxx Europe. Once the multivariate default distribution has been estimated, we analyse the distress dependence in the portfolio by computing indicators of systemic risk, such as the Stability Index, the Distress Dependence Matrix and the Probability of Cascade Effects.
|Date of creation:||Nov 2012|
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- 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.
- Donnelly, Catherine & Embrechts, Paul, 2010. "The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 40(01), pages 1-33, May.
- Elisa Luciano, 2007. "Copula-Based Default Dependence Modelling: Where Do We Stand?," ICER Working Papers - Applied Mathematics Series 21-2007, ICER - International Centre for Economic Research.
- Viktoriya Masol & Wim Schoutens, 2011. "Comparing alternative Levy base correlation models for pricing and hedging CDO tranches," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 763-773.
- Barbara Choros-Tomczyk & Wolfgang Karl HÃ¤rdle & Ludger Overbeck, 2012.
"Copula Dynamics in CDOs,"
SFB 649 Discussion Papers
SFB649DP2012-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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