IRB Asset and Default Correlation: Rationale for the Macroprudential Mark-Ups to the IRB Risk-Weights
Tóm tắt
There is a vast amount of literature criticizing the Basel Committee approach to the credit risk regulation, more specifically, the Internal Ratings-Based (IRB), as an excessively conservative one. However, the novelty of the current paper is that we identify when the IRB approach is too lax, i.e., we are able to present cases with the material credit risk underestimation. We show that the portfolio default rate (DR) depends on two parameters: probability of default (PD) and default correlation. Inversely, we offer a reproducible approach on how to derive the default correlation from historical data. Then it also depends on two parameters: PD and the historical DR variance. However, the IRB approach previewed only PD (and asset class) as the correlation determinants, neglecting the second contributor (DR variance). Hence, we demonstrate that when the actual DR variance exceeds the mean DR value, IRB may result in the credit risk underestimation. The almost two-fold underestimation is found for the credit cards (qualified revolving retail loans) asset class. The paper offers a practical solution how to adjust the revealed credit risk underestimation. The macroprudential add-ons to IRB risk-weights might be a workable solution format. Opinions expressed in the paper are solely those of the author and may not necessarily reflect the official position of the affiliated institution. Bank of Russia neither assumes any responsibility for the publication.
Tài liệu tham khảo
Aramonte, S., and F. Avalos. 2020. Corporate credit markets after the initial pandemic shock. Retrieved from BIS Bulletin No 26: https://www.bis.org/publ/bisbull26.htm
Bakbergenuly, I., E. Kulinskaya, and S. Morgenthaler. 2016. Inference for binomial probability based on dependent Bernoulli random variables with application to meta-nalaysis and group-level studies. Biometrical Journal 4 (58): 896–914.
Baldwin, K., M. Alhalboni, and M.H. Helmi. 2019. A structural model of “alpha” for the capital adequacy ratios of Islamic banks. Journal of International Financial Markets, Institutions and Money 60: 267–283.
Basten, C. 2020. Higher bank capital requirements and mortgage pricing: Evidence from the counter-cyclical capital buffer. Review of Finance 24 (2): 453–495.
BCBS. 1988. International convergence of capital measurement and capital standards (updated to april 1998). Retrieved from Basel Committee on Banking Supervision: https://www.bis.org/publ/bcbsc111.pdf. Accessed 25 Dec 2019.
BCBS. 2000. Range of Practice in Banks' Internal Ratings Systems. Retrieved from Basel Committee on Banking Supervision: https://www.bis.org/publ/bcbs66.htm. Accessed 25 Dec 2019.
BCBS. 2004. Basel II: International Convergence of Capital Measurement and Capital Standards: a Revised Framework. Retrieved from Basel Committee on Banking Supervision: https://www.bis.org/publ/bcbs107.htm. Accessed 27 Sept 2004.
BCBS. 2005a. Studies on the Validation on Internal Rating Systems. Retrieved from Basel Committee on Banking Supervision: https://www.bis.org/publ/bcbs_wp14.htm. Accessed 25 Dec 2019.
BCBS. 2005c. An Explanatory Note on the Basel II IRB Risk Weight Functions. Retrieved from Basel Committee on Banking Supervision: http://www.bis.org/bcbs/irbriskweight.htm. Accessed 12 Nov 2019.
BCBS. 2006. Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework - Comprehensive Version. Retrieved from Basel Committee on Banking Supervision: https://www.bis.org/publ/bcbs128.htm. Accessed 27 Sept 2006.
BCBS. 2017. Basel III: Finalising post-crisis reforms. Retrieved from Basel Committee on Banking Supervision: https://www.bis.org/bcbs/publ/d424.htm. Accessed 12 Nov 2019.
BCBS. 2019. Consolidated Basel Framework. Consultative Document. Retrieved from Basel Committee on Banking Supervision: https://www.bis.org/bcbs/publ/d462.pdf. Accessed 25 Dec 2019.
Berardi, A., S. Ciraolo, and M. Trova. 2004. Predicting default probabilities and implementing trading strategies for emerging markets bond portfolios. Emerging Markets Review 5: 447–469.
BIS. (2020, February 19). Measuring the effectiveness of macroprudential policies using supervisory bank-level data. Retrieved from Bank for International Settlements (Asian Office) Research And Publications: https://www.bis.org/publ/bppdf/bispap110.htm
Blochwitz, S., Martin, M., & Wehn, C. (2006). Statistical Appoaches to PD Validation. In B. Engelmann, & R. Rauhmeier (Eds.), The Basel II Risk Parameters. Estimation, Validation, Stress-Testing - with Applications to Loan Risk Management (pp. 289–306). London: Springer.
Bluhm, C., L. Overbeck, and C. Wagner. 2003. An Introduction to Credit Risk Modeling, 1st ed. Boca Raton: Chapman & Hall.
Borio, C. 2003. Towards a macroprudential framework for financial supervision and regulation? Retrieved from Monetary and Economic Department: https://www.bis.org/publ/work128.pdf
Budnik, K., and M. Jasova. (2018). The effect of macroprudential policies on credit developments in Europe 1995–2017. Retrieved from Joint European Central Bank and Central Bank of Ireland research workshop "Macroprudential policy: from research to implementation" (Dublin, Central Bank of Ireland): https://www.ecb.europa.eu/pub/conferences/shared/pdf/20180710_ecb_cbi_macroprudential_research_workshop_content/Katarzyna_Budnik-Presentation.pdf
Chiu, M., K. Jackson, and A. Kreinin. 2017. Correlated multivariate Poisson processes and extreme measures. Model Assisted Statistics and Applications 12: 369–385.
Clement, P. 2010. The term “macroprudential”: origins and evolution. Retrieved from BIS Quarterly Review: https://www.bis.org/publ/qtrpdf/r_qt1003h.pdf
Crockett, A. 2000. Marrying the micro- and macro-prudential dimensions of financial stability. Retrieved from Speech at the Eleventh International Conference of Banking Supervisors, Basel: https://www.bis.org/review/r000922b.pdf
da Silveira Barbedo, C.H., and E.F. Lemgruber. 2009. A down-and-out exchange option model with jumps to evaluate firms’ default probabilities in Brazil. Emerging Markets Review 10: 179–190.
Danilova, E., and M. Morozov. (2017). The macroprudential policy framework in Russia. Retrieved from BIS Papers No. 94. Macroprudential frameworks, implementation and relationship with other policies: https://www.bis.org/publ/bppdf/bispap94.pdf
Dautović, E. 2019. Has regulatory capital made banks safer? Skin in the game vs moral hazard. Retrieved from European Systemic Risk Board Working Paper Series No 91: https://www.esrb.europa.eu/pub/pdf/wp/esrb.wp91~4c70a46630.en.pdf
Duellmann, K., J. Kull, and M. Kunisch. 2010. Estimating asset correlations from stock prices or default rates—Which method is superior? Journal of Economic Dynamics and Control 34: 2341–2357.
Duffie, D., and K. Singleton. 1999. Simulating Correlated Defaults. https://www.darrellduffie.com/uploads/working/DuffieSingleton1999.pdf. Accessed 15 Dec 2019.
Duffie, D., & Singleton, K. (2003). Credit Risk. Pricing, Measurement, and Management. Princeton: Stanford University.
Fantazzini, D. 2009. Credit risk management (continuation) [in Russian]. Applied Econometrics 13 (1): 105–138.
Foulcher, S., C. Gouriéroux, and A. Tiomo. 2005. Latent Variable Approach to Modelling Dependence of Credit Risks: Application to French Firms and Implications for Regulatory Capital, 05–1. Paris: CREF.
Gambacorta, L., and A. Murcia. 2020. The impact of macroprudential policies in Latin America: An empirical analysis using credit registry data. Journal of Financial Intermediation. https://doi.org/10.1016/j.jfi.2019.04.004.
Gordy, M. 2000. A comparative anatomy of credit risk models. Journal of Banking and Finance 24: 119–149.
Gordy, M. B., and Heitfield, E. 2010. Small-Sample Estimation of Models of Portfolio Credit Risk. In M. Kijima, C. Hara, K. Tanaka, & Y. Muromachi (Eds.), Recent Advances in Financial Engineering: The Proceedings of the KIER-TMU International Workshop on Financial Engineering 2009 (pp. 43–63).
Ivanova, N., Andreev, M., Sinyakov, A., and Shevchuk, I. (2019). Review of Bank of Russia Conference on ‘Macroprudential Policy Effectiveness: Theory and Practice’. Russian Journal of Money and Finance, 3, 89–121.
Kahou, M.E., and A. Lehar. 2017. Macroprudential policy: A review. Journal of Financial Stability 29: 92–105.
Khorasgani, A., and Gupta, J. 2017. Estimating Reserve Requirement for Credit Portfolio of UK SMEs. Retrieved from SSRN (https://doi.org/10.2139/ssrn.2961243): https://www.researchgate.net/publication/324664468_Estimating_Reserve_Requirement_for_Credit_Portfolio_of_UK_SMEs
Khotulev, I., and K. Styrin. 2020. Optimal monetary and macroprudential policies for financial stability in a commodity-exporting economy. Russian Journal of Money and Finance 79 (2): 3–42.
Kim, S., and J. Oh. 2020. Macroeconomic effects of macroprudential policies: Evidence from LTV and DTI policies in Korea. Japan and the World Economy. https://doi.org/10.1016/j.japwor.2020.100997.
Kruppa, J., B. Lepenies, and K. Jung. 2018. A genetic algorithm for simulating correlated binary data from biomedical research. Computers in Biology and Medicine 92: 1–8. https://doi.org/10.1016/j.compbiomed.2017.10.023.
Kupiec, P. H. 2009. How Well Does the Vasicek-Basel AIRB Model Fit the Data? Evidence from a Long Time Series of Corporate Credit Rating Data. Retrieved from FDIC Center for Financial Research Working Paper No. 2009-10.
Levy, A. 2008. An overview of modeling credit portfolios. Modeling Methodology. Retrieved from Moody's KMV.
Li, D. 2000. On default correlation: A copula function approach. Journal of Fixed Income 9 (4): 43–54.
Li, X., Y. Shang, and Z. Su. 2015. Semiparametric estimation of default probability: Evidence from the Prosper online credit market. Economics Letters 127: 54–57. https://doi.org/10.1016/j.econlet.2014.11.033.
Lopez, J. A. 2002. The Empirical Relationship between Average Asset Correlation, Firm Probability of Default and Asset Size. https://www.bis.org/bcbs/events/b2ealop.pdf. Accessed 09 Jan 2020.
Lubis, A., C. Alexiou, and J.G. Nellis. 2019. What Can We Learn from the Implementation of Monetary and Macroprudential Policies: A Systematic Literature Review. Journal of Economic Surveys 33 (4): 1123–50.
Lunn, A., and S. Davies. 1998. A note on generating correlated binary variables. Biometrika 2 (85): 487–490.
McCann, F., and C. O’Toole. 2019. Cross-border macroprudential policy spillovers and bank risk-taking. International Journal of Central Banking 15 (4): 267–311.
Merika, A., H. Penikas, and I. Negkakis. 2021. Stress-testing and credit risk revisited: A shipping sector application. International Journal of Banking, Accounting and Finance 12 (4): 389–403.
Merton, R. 1974. On the pricing of corporate debt: The risk structure of interest. Journal of Finance 29: 449–470.
Miller, G.E. 1991. Asymptotic test statistics for coefficient of variation. Commuinications in Statistics - Mathematics Methodology 20 (10): 3351–3363.
Moody's. 2018. Cross-Sector: Annual Default Study: Corporate Default and Recovery Rates, 1920–2017. https://www.moodys.com/researchdocumentcontentpage.aspx?docid=PBC_1112754. Accessed 20 Dec 2019
Nagpal, K., and R. Bahar. 2001. Measuring default correlation. Risk 14 (3): 129–132.
Ozdemir, B., and P. Miu. 2009. Basel II Implementation. A Guide to Developing and Validating a Compliant Internal Risk Rating System. New York: McGrawHill.
Patel, K., and R. Pereira. 2008. The determinants of default correlations. Advances in Econometrics 22: 123–158.
Preisser, J.S., and B.F. Qaqish. 2014. A comparison of methods for simulating correlated binary variables with specified marginal means and correlations. Journal of Statistical Computation and Simulation 84 (11): 2441–2452.
S&P Global Ratings. 2019. 2018 Annual Global Corporate Default And Rating Transition Study. https://www.spratings.com/documents/20184/774196/2018AnnualGlobalCorporateDefaultAndRatingTransitionStudy.pdf. Accessed 20 Dec 2019.
Schoenmaker, D. 2014. Macroprudentialism. Retrieved from https://voxeu.org/system/files/epublication/macroprudentialism_VoxEU_0.pdf
Van Der Geest, P.A. 2005. The binomial distribution with dependent Bernoulli trials. Journal of Statistical Computation and Simulation 2 (75): 141–154.
Vasicek, O. 2002. The Distribution of Loan Portfolio Value. Risk, 160–162. Retrieved July 20, 2018, from Reprinted in Risk in December 2002: https://www.bankofgreece.gr/MediaAttachments/Vasicek.pdf
Vozzella, P., and G. Gabbi. 2010. Default and Asset Correlation: An Empirical Study for Italian SMEs. Retrieved from SSRN: https://ssrn.com/abstract=1532222
Witt, G. 2004. Moody’s Correlated Binomial Default Distribution. Retrieved from Structured Finance. Rating Methodology: http://fcic-static.law.stanford.edu/cdn_media/fcic-testimony/2010-0602-exhibit-binomial.pdf
Witt, G. 2014. A simple distribution for the sum of correlated, exchangeable binary data. Communications in Statistics - Theory and Methods 43: 4265–4280.
Wunderer, C. 2019. Asset correlation estimation for inhomogeneous exposure pools. Journal of Credit Risk 15 (3): 1–19.
Yarba, I., and Z.N. Güner. 2020. Uncertainty, macroprudential policies and corporate leverage: Firm-level evidence. Central Bank Review 20: 33–42.
Zaigraev, A., and S. Kaniovski. 2013. A note on the probability of at least k successes in n correlated binary trials. Operations Research Letters 41 (1): 116–120.