Modeling Portfolio Loss by Interval Distributions

Yang, Bill Huajian and Yang, Jenny and Yang, Haoji (2020): Modeling Portfolio Loss by Interval Distributions. Published in: Big Data and Information Analytics , Vol. 5, No. 1 (4 August 2020): pp. 1-13.

Abstract

Models for a continuous risk outcome has a wide application in portfolio risk management and capital allocation. We introduce a family of interval distributions based on variable transformations. Densities for these distributions are provided. Models with a random effect, targeting a continuous risk outcome, can then be fitted by maximum likelihood approaches assuming an interval distribution. Given fixed effects, regression function can be estimated and derived accordingly when required. This provides an alternative regression tool to the fraction response model and Beta regression model.

• Item Type: MPRA Paper
• Language: English
• Keywords: Interval distribution, model with a random effect, tailed index, expected shortfall, heteroscedasticity, Beta regression model, fraction response model, maximum likelihood.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs

References

[1] Basel Committee on Banking Supervision (2005). An Explanatory Note on the Basel II IRB Risk Weight Functions, July 2005.

[2] Basel Committee on Banking Supervision (2015). Guidance on credit risk and accounting for expected credit loss, December 2015.

[3] Basel Committee on Banking Supervision (2019). Minimum capital requirements for market risk, January 2019.

[4] Cribari-Neto, F. and Zeileis, A (2020). Beta Regression in R, Cran.R-Project.Org.

[5] Friedman, J. and Hastie, T. and Tibshirani, R. (2008). The Elements of Statistical Learning, 2nd edition,Springer.

[6] Gourieroux, C., and Monfort, A. and Trognon, A. (1984). Pseudo-maximum likelihood methods: theory, Econometrica, 52, 681 -700.

[7] Huang, X., Oosterlee, C. W., Mesters, M. (2007). Computation of VaR and VaR contribution in the Vasicek portfolio credit loss model: a comparative study. Journal of Credit Risk, Vol 3 (3), September 2007. DOI: 10.21314.JCR.2007.048.

[8] Mullahy, J. (1990). Regression models and transformations for Beta-distributed outcomes, mimeo, Trinity College Department of Economics.

[9] Murphy, K. (2012). Machine Learning: A Probabilistic Perspective. MIT. ISBN 978-0262018029.

[10] Papke, L. E., Wooldrige, J. M (1996). Econometric methods for fraction response variables with application to 401 (k) plan participation rates, Journal of Applied Econometrics, Vol. 11, 619-632.

[11] Ramponi, F. A. and Campi, M. C. (2018). Expected shortfall: Heuristics and certificates, European Journal of Operational Research, Volume 267, Issue 3, June 2018, pp. 1003-1013.

[12] Rosen, D. and Saunders, D. (2009). Analytical methods for hedging systematic credit risk with linear factor portfolios. Journal of Economic Dynamics & Control, 33 (2009), pp. 37-52.

[13] Vasicek, O. (1991). Limiting Loan Loss Probability Distribution, KMV Corporation.

[14] Vasicek, O. (2002). Loan portfolio value. Risk, December 2002, pp. 160 - 162.

[15] Wolfinger, R. (2008). Fitting Nonlinear Mixed Models with the New NLMIXED Procedure. SAS Institute Inc.

[16] Wu, Biao (2019). The Probability of Default Distribution of Heterogeneous Loan Portfolio, Current Analysis on Economics & Finance, May 2019, Vol. 1, 88-95.

[17] Yamai, Y. and Yoshiba, T. (2002). Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization, Monetary and Economic Studies, 2002, vol. 20, issue 1, 87-121.

[18] Yang, B. H. (2013). Estimating Long-Run PD, Asset Correlation, and Portfolio Level PD by Vasicek Models, Journal of Risk Model Validation, Volume 7 (4), pp. 3-19.

[19] Yang, B. H. and Wu, Biao and Cui, Kaijie and Du, Zunwei and Fei, Glenn (2020). IFRS9 Expected Credit Loss Estimation: Advanced Models for Estimating Portfolio Loss and Weighting Scenario Losses, Vol. 14, No. 1, pp: 19-34, DOI: 10.21314/JRMV.2020.217.