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Dependence of defaults and recoveries in structural credit risk models

  • Schäfer, Rudi
  • Koivusalo, Alexander F.R.
Registered author(s):

    The current research on credit risk is primarily focused on modelling default probabilities. Recovery rates are often treated as an afterthought; they are modelled independently, in many cases they are even assumed to be constant. This despite their pronounced effect on the tail of the loss distribution. Here, we take a step back, historically, and start again from the Merton model, where defaults and recoveries are both determined by an underlying process. Hence, they are intrinsically connected. For the diffusion process, we can derive the functional relation between expected recovery rate and default probability. This relation depends on a single parameter only. In Monte Carlo simulations we find that the same functional dependence also holds for jump-diffusion and GARCH processes. We discuss how to incorporate this structural recovery rate into reduced-form models, in order to restore essential structural information which is usually neglected in the reduced-form approach.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0264999312002751
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    Article provided by Elsevier in its journal Economic Modelling.

    Volume (Year): 30 (2013)
    Issue (Month): C ()
    Pages: 1-9

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    Handle: RePEc:eee:ecmode:v:30:y:2013:i:c:p:1-9
    DOI: 10.1016/j.econmod.2012.08.033
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/30411

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    1. Chen, Cho-Jieh & Panjer, Harry, 2003. "Unifying discrete structural models and reduced-form models in credit risk using a jump-diffusion process," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 357-380, October.
    2. Rudi Sch\"afer & Markus Sj\"olin & Andreas Sundin & Michal Wolanski & Thomas Guhr, 2007. "Credit risk - A structural model with jumps and correlations," Papers 0707.3478, arXiv.org, revised Jul 2007.
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    4. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409 World Scientific Publishing Co. Pte. Ltd..
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    6. Edward I. Altman & Brooks Brady & Andrea Resti & Andrea Sironi, 2005. "The Link between Default and Recovery Rates: Theory, Empirical Evidence, and Implications," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2203-2228, November.
    7. Schäfer, Rudi & Sjölin, Markus & Sundin, Andreas & Wolanski, Michal & Guhr, Thomas, 2007. "Credit risk—A structural model with jumps and correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 533-569.
    8. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453 World Scientific Publishing Co. Pte. Ltd..
    9. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    10. Alexander Becker & Alexander F. R. Koivusalo & Rudi Sch\"afer, 2012. "Empirical Evidence for the Structural Recovery Model," Papers 1203.3188, arXiv.org.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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