Default Clustering in Large Pools: Large Deviations
We study large deviations and rare default clustering events in a dynamic large heterogeneous portfolio of interconnected components. Defaults come as Poisson events and the default intensities of the different components in the system interact through the empirical default rate and via systematic effects that are common to all components. We establish the large deviations principle for the empirical default rate for such an interacting particle system. The rate function is derived in an explicit form that is amenable to numerical computations and derivation of the most likely path to failure for the system itself. Numerical studies illustrate the theoretical findings. An understanding of the role of the preferred paths to large default rates and the most likely ways in which contagion and systematic risk combine to lead to large default rates would give useful insights into how to optimally safeguard against such events.
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- Dai Pra, Paolo & Tolotti, Marco, 2009.
"Heterogeneous credit portfolios and the dynamics of the aggregate losses,"
Stochastic Processes and their Applications,
Elsevier, vol. 119(9), pages 2913-2944, September.
- Paolo Dai Pra & Marco Tolotti, 2008. "Heterogeneous credit portfolios and the dynamics of the aggregate losses," Papers 0806.3399, arXiv.org.
- Konstantinos Spiliopoulos & Justin A. Sirignano & Kay Giesecke, 2013. "Fluctuation Analysis for the Loss From Default," Papers 1304.1420, arXiv.org, revised Feb 2015.
- Amir Dembo & Jean-Dominique Deuschel & Darrell Duffie, 2004. "Large portfolio losses," Finance and Stochastics, Springer, vol. 8(1), pages 3-16, January.
- Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
- Paolo Dai Pra & Wolfgang J. Runggaldier & Elena Sartori & Marco Tolotti, 2007. "Large portfolio losses: A dynamic contagion model," Papers 0704.1348, arXiv.org, revised Mar 2009.
- Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
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