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Computing optimal recovery policies for financial markets

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  • Fred E. Benth

    ()
    (Department of Mathematics, CMA, University of Oslo, Norway.)

  • Geir Dahl

    ()
    (Department of Mathematics and Department of Informatics, CMA, University of Oslo, Norway.)

  • Carlo Mannino

    ()
    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

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    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 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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    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/wpaper/2010-20.pdf
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    Bibliographic Info

    Paper 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.

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    Date of creation: 2010
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    Handle: RePEc:aeg:wpaper:2010-20

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    Keywords: Financial models; discrete optimization; bilevel programming; Markov random field;

    References

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    1. 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.
    2. I. Onur Filiz & Xin Guo & Jason Morton & Bernd Sturmfels, 2008. "Graphical models for correlated defaults," Papers 0809.1393, arXiv.org.
    3. 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.
    4. 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.
    5. Giesecke, Kay & Weber, Stefan, 2006. "Credit contagion and aggregate losses," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 741-767, May.
    6. 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.
    7. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
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