Large Portfolio Asymptotics for Loss From Default
We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear SPDE, and the moments of the limiting measure are shown to satisfy an infinite system of SDEs. The solution to this system leads to %the solution to the SPDE through an inverse moment problem, and to the distribution of the limiting portfolio loss, which we propose as an approximation to the loss distribution for a large portfolio. Numerical tests illustrate the accuracy of the approximation, and highlight its computational advantages over a direct Monte Carlo simulation of the original stochastic system.
|Date of creation:||Sep 2011|
|Date of revision:||Feb 2015|
|Publication status:||Published in Mathematical Finance, Volume 25, Number 1, 2015, pages 77-114|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
- 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.
- Michael B. Gordy, 2002.
"A risk-factor model foundation for ratings-based bank capital rules,"
Finance and Economics Discussion Series
2002-55, Board of Governors of the Federal Reserve System (U.S.).
- Gordy, Michael B., 2003. "A risk-factor model foundation for ratings-based bank capital rules," Journal of Financial Intermediation, Elsevier, vol. 12(3), pages 199-232, July.
- 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.
- Sanjiv Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2006.
"Common Failings: How Corporate Defaults are Correlated,"
NBER Working Papers
11961, National Bureau of Economic Research, Inc.
- Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, 02.
- Lucas, André & Klaassen, Pieter & Spreij, Peter, 1999.
"An analytic approach to credit risk of large corporate bond and loan portfolios,"
Serie Research Memoranda
0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
- Lucas, Andre & Klaassen, Pieter & Spreij, Peter & Straetmans, Stefan, 2001. "An analytic approach to credit risk of large corporate bond and loan portfolios," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1635-1664, September.
- Nick Bush & Ben M. Hambly & Helen Haworth & Lei Jin & Christoph Reisinger, 2011. "Stochastic evolution equations in portfolio credit modelling with applications to exotic credit products," Papers 1103.4947, arXiv.org, revised Apr 2011.
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