Computing Optimal Recovery Policies for Financial Markets

Fred E. Benth (), Geir Dahl () and Carlo Mannino ()
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Fred E. Benth: Department of Mathematics, Centre of Mathematics for Applications, University of Oslo, N-0316 Oslo, Norway
Geir Dahl: Department of Mathematics and Department of Informatics, Centre of Mathematics for Applications, University of Oslo, N-0316 Oslo, Norway
Carlo Mannino: Department of Computer Science, University of Rome “La Sapienza,” Rome, Italy; and Centre of Mathematics for Applications, N-0316 Oslo, Norway

Operations Research, 2012, vol. 60, issue 6, 1373-1388

Abstract: The 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 in which uncertainty in default probabilities incorporates experts' 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 and give a practical procedure for estimation of model parameters. 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.

Keywords: financial models; discrete optimization; bilevel programming; Markov random field (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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