Computing optimal recovery policies for financial markets
AbstractThe current financial crisis motivates the study of correlated defaults in financial systems. In this paper we focus on such a model which is based on Markov random fields. This is a probabilistic model where uncertainty in default probabilities incorporates expert's opinions on the default risk (based on various credit ratings). We consider a bilevel optimization model for finding an optimal recovery policy: which companies should be supported given a fixed budget. This is closely linked to the problem of finding a maximum likelihood estimator of the defaulting set of agents, and we show how to compute this solution efficiently using combinatorial methods. We also prove properties of such optimal solutions. A practical procedure for estimation of model parameters is also given. Computational examples are presented and experiments indicate that our methods can find optimal recovery policies for up to about 100 companies. The overall approach is evaluated on a real-world problem concerning the major banks in Scandinavia and public loans. To our knowledge this is a first attempt to apply combinatorial optimization techniques to this important, and expanding, area of default risk analysis.
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Bibliographic InfoPaper provided by Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza" in its series DIS Technical Reports with number 2010-20.
Date of creation: 2010
Date of revision:
Financial models; discrete optimization; bilevel programming; Markov random field;
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- I. Onur Filiz & Xin Guo & Jason Morton & Bernd Sturmfels, 2008. "Graphical models for correlated defaults," Papers 0809.1393, arXiv.org.
- René Carmona & Jean-Pierre Fouque & Douglas Vestal, 2009. "Interacting particle systems for the computation of rare credit portfolio losses," Finance and Stochastics, Springer, vol. 13(4), pages 613-633, September.
- Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, vol. 50(1), pages 53-85, March.
- Giesecke, Kay & Weber, Stefan, 2006. "Credit contagion and aggregate losses," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 741-767, May.
- Merton, Robert C, 1974.
"On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,"
Journal of Finance,
American Finance Association, vol. 29(2), pages 449-70, May.
- Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
- Martine Labbé & Patrice Marcotte & Gilles Savard, 1998. "A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1608-1622, December.
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