Default probability estimation in small samples - with an application to sovereign bonds

Orth, Walter (2011): Default probability estimation in small samples - with an application to sovereign bonds.

Abstract

In small samples and especially in the case of small true default probabilities, standard approaches to credit default probability estimation have certain drawbacks. Most importantly, standard estimators tend to underestimate the true default probability which is of course an undesirable property from the perspective of prudent risk management. As an alternative, we present an empirical Bayes approach to default probability estimation and apply the estimator to a comprehensive sample of Standard & Poor's rated sovereign bonds. We further investigate the properties of a standard estimator and the empirical Bayes estimator by means of a simulation study. We show that the empirical Bayes estimator is more conservative and more precise under realistic data generating processes.

• Item Type: MPRA Paper
• Language: English
• Keywords: Low-default portfolios; empirical Bayes; sovereign default risk; Basel II
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C41 - Duration Analysis ; Optimal Timing Strategies; G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets; G - Financial Economics > G2 - Financial Institutions and Services > G28 - Government Policy and Regulation; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General

References

Altman, E. I. (1989). Measuring corporate bond mortality and performance. Journal of Finance, 44(4), 909–922.

BBA (British Bankers’ Association, London Investment Banking Association, International Swaps and Derivatives Association) (2004). The IRB Approach for Low Default Portfolios (LDPs) - Recommendations of the Joint BBA, LIBA, ISDA Industry Working Group.

BCBS (Basel Committee on Banking Supervision) (2005). Validation of Low-Default Portfolios in the Basel II Framework. Basel Committee Newsletter No. 6 (September 2005).

BCBS (Basel Committee on Banking Supervision) (2006). International Convergence of Capital Measurement and Capital Standards: A Revised Framework.

BCBS (Basel Committee on Banking Supervision) (2009). Guiding Principles for the Replacement of IAS 39. Available at http://www.bis.org/publ/bcbs161.htm.

BCBS (Basel Committee on Banking Supervision) (2010). Group of Governors and Heads of Supervision Announces Higher Global Minimum Capital Standards. Press release, September 12, 2010.

Benjamin, N., Cathcart, A., & Ryan, K. (2006). Low Default Portfolios: A Proposal for Conservative Estimation of Default Probabilities. Financial Services Authority, London. Discussion Paper.

Birnbaum, A. (1963). Median-unbiased estimators. Bulletin of Mathematical Statistics, 11, 25–34.

Carlin, B. P. & Louis, T. A. (2008). Bayesian Methods for Data Analysis. Boca Raton: CRC Press, 3rd edition.

Casella, G. (1985). An introduction to empirical Bayes analysis. The American Statistician, 39(2), 83–87.

Christensen, J. H., Hansen, E., & Lando, D. (2004). Confidence sets for continous-time rating transition probabilities. Journal of Banking & Finance, 28, 2575–2602.

Cutler, S. J. & Ederer, F. (1958). Maximum utilization of the life table method in analyzing survival. Journal of Chronic Diseases, 8(6), 699–712.

Fuertes, A.-M. & Kalotychou, E. (2007). On sovereign credit migration: A study of alternative estimators and rating dynamics. Computational Statistics & Data Analysis, 51, 3448–3469.

Gupton, G. M., Finger, C. M., & Bhatia, M. (1997). CreditMetricsTM - Technical Document. J.P. Morgan, New York.

Hamilton, D. T. & Cantor, R. (2006). Measuring Corporate Default Rates. Moody’s Investors Service. Special Comment.

Hanson, S. & Schuermann, T. (2006). Confidence intervals for probabilities of default. Journal of Banking & Finance, 30, 2281–2301.

Hjort, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Annals of Statistics, 18(3), 1259–1294.

Johansen, S. (1978). The Product Limit estimator as Maximum Likelihood estimator. Scandinavian Journal of Statistics, 5(4), 195–199.

Kiefer, N. M. (2009). Default estimation for low-default portfolios. Journal of Empirical Finance, 16(1), 164–173.

Kiefer, N. M. (2010). Default estimation and expert information. Journal of Business & Economic Statistics, 28(2), 320–328.

Kiefer, N. M. & Larson, C. E. (2003). Biases in Default Estimation and Capital Allocations under Basel II. Working paper.

Kleinman, J. C. (1973). Proportions with extraneous variance: Single and independent sample. Journal of the American Statistical Association, 68(341), 46–54.

Kurbat, M. & Korablev, I. (2002). Methodology for Testing the Level of the EDF Credit Measure. Moody’s KMV Technical Report No. 020729.

Lando, D. & Skodeberg, T. M. (2002). Analyzing Rating Transitions and Rating Drift with Continous Observations. Journal of Banking & Finance, 26, 423–444.

Lawrenz, J. (2008). Assessing the estimation uncertainty of default probabilities. Kredit und Kapital, 41(2), 217–238.

Pluto, K. & Tasche, D. (2006). Estimating probabilities of default for low default portfolios. In B. Engelmann & R. Rauhmeier (Eds.), The Basel II Risk Parameters (pp. 79–103). Berlin: Springer.

Standard & Poor’s (2011a). Sovereign Defaults and Rating Transition Data, 2010 Update. Publication date: February 23, 2011.

Standard & Poor’s (2011b). Sovereign Rating and Country T&C Assessment Histories. Publication date: June 3, 2011.

Standard & Poor’s (2011c). Standard & Poor’s Noninvestment Grade Sovereign Debt Recovery Ratings: 2011 Update. RatingsDirect, Global Credit Portal: March 29, 2011.