Dependent default and recovery: Markov chain Monte Carlo study of downturn Loss Given Default credit risk model

There is empirical evidence that recovery rates tend to go down just when the number of defaults goes up in economic downturns. This has to be taken into account in estimation of the capital against credit risk required by Basel II to cover losses during the adverse economic downturns; the so-called ``downturn Loss Given Default" requirement. This article presents a methodology for estimation of the Loss Given Default credit risk model with the default and recovery dependent via the latent systematic risk factor using a Bayesian inference approach and Markov chain Monte Carlo method. This approach allows joint estimation of all model parameters and latent systematic factor, and all relevant uncertainties. For illustration, we fit the model using Moody's annual default and recovery rates for corporate bonds for the period 1982--2010. References Basel Committee on Banking Supervision. Guidance on Paragraph 468 of the Framework Document . Bank for International Settlements, Basel, July 2005. http://www.bis. org/publ/bcbs115.htm K. Dullmann and M. Trapp. Systematic risk in recovery rates - an empirical analysis of us corporate credit exposures. Discussion Paper, Series2: Banking and Financial Supervision , pages 1--44, 2004. http://papers.ssrn. com/sol3/papers.cfm? abstract_id=494462 J. Frye. Depressing recoveries. Risk , 13:106--111, 2000. http://www.risk. net/data/Pay_per_view/risk/technical/2000/risk_1100_creditrisk. pdf M. Gordy. A risk-factor foundation for ratings-based bank capital rules. Finance and Economics Discussion Series 2002-55, Washington: Board of Governors of the Federal Reserve System , 2002. doi:10.2139/ssrn.361302 X. Luo, P. V. Shevchenko, and J. Donnelly. Addressing impact of truncation and parameter uncertainty on operational risk estimates. The Journal of Operational Risk , 2(4):3--26, 2007. http://www.risk. net/journal-of-operational-risk/journal/2160945/journal-operational-risk-volume-number-winter-2007 Moody's. Corporate default and recovery rates, 1920--2010. Technical report, February 2011. http://www.moodys. com G. W. Peters, P. V. Shevchenko, and M. V. Wuthrich. Dynamic operational risk: modelling dependence and combining different data sources of information. The Journal of Operational Risk , 4(2):69--104, 2009. http://www.risk. net/journal-of-operational-risk/journal/2160936/journal-operational-risk-volume-number-summer-2009 G. W. Peters, P. V. Shevchenko, and M. V. Wuthrich. Model uncertainty in claims reserving within Tweedie's compound poisson models. ASTIN Bulletin , 39(1):1--33, 2009. doi:10.2143/AST.39. 1.2038054 M. Pykhtin. Unexpected recovery risk. Risk , 16(8):74--78, 2003. http://www.risk. net/risk-magazine/technical-paper/1530263/unexpected-recovery-risk C. P. Robert. The Bayesian Choice . Springer Verlag, New York, 2001. G. O. Roberts and J. S. Rosenthal. Optimal scaling for various Metropolis-Hastings algorithms. Statistical Science , 16:351--367, 2001. doi:10.1214/ss/1015346320 D. Rosch and H. Scheule. A multifactor approach for systematic default and recovery risk. The Journal of Fixed Income , 15(2):63--75, 2005. doi:10.3905/jfi.2005. 591610 P. V. Shevchenko. Estimation of operational risk capital charge under parameter uncertainty. The Journal of Operational Risk , 3(1):51--63, 2008. http://www.risk. net/journal-of-operational-risk/journal/2160943/journal-operational-risk-volume-number-spring-2008 P. V. Shevchenko. Modelling Operational Risk Using Bayesian Inference . Springer, Berlin, 2011. P. V. Shevchenko and G. Temnov. Modeling operational risk data reported above a time-varying threshold. The Journal of Operational Risk , 4(2):19--42, 2009. http://www.risk. net/journal-of-operational-risk/journal/2160936/journal-operational-risk-volume-number-summer-2009