Yang, Bill Huajian and Du, Zunwei (2015): Stress Testing and Modeling of Rating Migration under the Vasicek Model Framework  Empirical approaches and technical implementation. Published in: Journal of Risk Model Validation , Vol. 9, No. 2 (18. June 2015)

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Abstract
Under the Vasicek asymptotic single risk factor model, stress testing based on rating transition probability involves three components: the unconditional rating transition matrix, asset correlations, and stress testing factor models for systematic downgrade (including default) risk. Conditional transition probability for stress testing given systematic risk factors can be derived accordingly. In this paper, we extend Miu and Ozdemir’s work ([14]) on stress testing under this transition probability framework by assuming different asset correlation and different stress testing factor model for each nondefault rating. We propose two Vasicek models for each nondefault rating, one with a single latent factor for rating level asset correlation, and another multifactor Vasicek model with a latent effect for systematic downgrade risk. Both models can be fitted effectively by using, for example, the SAS nonlinear mixed procedure. Analytical formulas for conditional transition probabilities are derived. Modeling downgrade risk rather than default risk addresses the issue of low default counts for high quality ratings. As an illustration, we model the transition probabilities for a corporate portfolio. Portfolio default risk and credit loss under stress scenarios are derived accordingly. Results show, stresstesting models developed in this way demonstrate desired sensitivity to risk factors, which is generally expected.
Item Type:  MPRA Paper 

Original Title:  Stress Testing and Modeling of Rating Migration under the Vasicek Model Framework  Empirical approaches and technical implementation 
English Title:  Stress Testing and Modeling of Rating Migration under the Vasicek Model Framework  Empirical approaches and technical implementation 
Language:  English 
Keywords:  Stress testing, systematic risk, asset correlation, rating migration, Vasicek model, bootstrap aggregation 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C5  Econometric Modeling G  Financial Economics > G3  Corporate Finance and Governance G  Financial Economics > G3  Corporate Finance and Governance > G30  General G  Financial Economics > G3  Corporate Finance and Governance > G32  Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill G  Financial Economics > G3  Corporate Finance and Governance > G38  Government Policy and Regulation 
Item ID:  65168 
Depositing User:  Dr. Bill Huajian Yang 
Date Deposited:  23. Jun 2015 06:33 
Last Modified:  23. Jun 2015 06:49 
References:  [1] Basel Committee on Banking Supervision (2009). Principles for Sound Stress Testing Practices and Supervision [2] Belkin, B., Forest, L., and Suchover, S. (1998). A oneparameter representation of credit risk and transition matrices. Credit Metrics Monitor 1(3), 4656 [3] Blaschke, W., Jones , M. T., Majnoni, G., and Peria, S. M.(2001). Stress Testing of Financial Systems: An Overview of Issues, Methodologies, and FSAP Experiences,IMF Working Paper, WP/01/88 [4] Breiman, L. (1996). Bagging Predictors. Machine Learning 24: 123140 [5] Bunn, P. (2005). Stress testing as a tool for assessing systematic risks, Financial Stability Review, 2005:6,pp.116126 [6] Demey, P., Jouanin, J., Roget, C, and Roncalli, T.(2004). Maximum likelihood estimate of default correlations, Risk, November 2004 [7] Drehmann, M. (2008). Stress tests: Objectives, challenges and modelling choices,Economic Review, 2008:Vol 60 (2), pp. 6092 [8] Friedman, J., Hastie, T., and Tibshirani, R. (2008). The Elements of Statistical Learning, 2nd edition, Springer [9] Gordy, M. B. (2003). A riskfactor model foundation for ratingsbased bank capital rule. Journal of Financial Intermediation 12, pp.199232. [10] Gordy, M., Heitfield, E. (2002). Estimating default correlations from short panels of credit rating performance data. Federal Reserve Board Working paper, January 2002 [11] Jacobson, T., Linde, J., Roszbach, K. (2011) Firm Default and Aggregate Fluctuations,Board of Governors of the Federal Reserve System, August 2011 [12] Merton, R. (1974). On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance, Volume 29 (2), 449470 [13] Meyer, C. (2009). Estimation of intrasector asset correlation. The Journal of Risk Model validation, Volume 3 (3), Fall [14] Miu, P., Ozdemir, B. (2009). Stress testing probability of default and rating migration rate with respect to Basel II requirements, Journal of Risk Model Validation, Vol. 3 (4) Winter 2009, pp.338 [15] Miu, P., Ozdemir, B. (2008). Estimating and validating longrun probability of default with respect to Basel II requirements. The Journal of Risk Model validation, Volume 2/Number 2,341 [16] Pindyck, R. S., Rubinfeld, D. L. (1998). Econometric Models and Economic Forecasts,4th Edition, Irwin/McGrawHill [17] Rosen, D., Saunders, D. (2009). Analytical methods for hedging systematic credit risk with linear factor portfolios. Journal of Economic Dynamics & Control, 33 (2009), 3752 [18] Sorge, M. (2004). Stresstesting financial systems: an overview of current methodologies, BIS Working papers, No. 165 [19] Tarashev, N., Borio, C., and Tsatsaronis, K. (2010). Attributing systematic risk to individual institutions,” Technical Report Working Papers No 308,BIS, May 2010. [20] Vasicek, O. (2002). Loan portfolio value. RISK, December 2002, 160  162. [21] Wolfinger, R. (2008). Fitting Nonlinear Mixed Models with the New NLMIXED Procedure. SAS Institute Inc. [22] Yang, B. H. (2013). Estimating longrun probability of default, asset correlation and portfoliolevel probability of default using Vasicek models, Journal of Risk Model Validation, Winter 2013, pp.319 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/65168 