Smoothing Algorithms by Constrained Maximum Likelihood

Yang, Bill Huajian (2017): Smoothing Algorithms by Constrained Maximum Likelihood. Forthcoming in: Journal of Risk Model Validation (September 2017)

Abstract

In the process of loan pricing, stress testing, capital allocation, modeling of PD term structure, and IFRS9 expected credit loss estimation, it is widely expected that higher risk grades carry higher default risks, and that an entity is more likely to migrate to a closer non-default rating than a farther away non-default rating. In practice, sample estimates for rating level default rate or rating migration probability do not always respect this monotonicity rule, and hence the need for smoothing approaches. Regression and interpolation techniques are widely used for this purpose. A common issue with these approaches is that the risk scale for the estimates is not fully justified, leading to a possible bias in credit loss estimates. In this paper, we propose smoothing algorithms for rating level PD and rating migration probability. The smoothed estimates obtained by these approaches are optimal in the sense of constrained maximum likelihood, with a fair risk scale determined by constrained maximum likelihood, leading to more robust credit loss estimation. The proposed algorithms can be easily implemented by a modeller using, for example, the SAS procedure PROC NLMIXED. The approaches proposed in this paper will provide an effective and useful smoothing tool for practitioners in the field of risk modeling.

• Item Type: MPRA Paper
• Language: English
• Keywords: Credit loss estimation, risk scale, constrained maximum likelihood, PD term structure, rating migration probability
• 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 > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General; 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 > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C54 - Quantitative Policy 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 > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit; G - Financial Economics > G3 - Corporate Finance and Governance > G31 - Capital Budgeting ; Fixed Investment and Inventory Studies ; Capacity; G - Financial Economics > G3 - Corporate Finance and Governance > G38 - Government Policy and Regulation; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O32 - Management of Technological Innovation and R&D; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O33 - Technological Change: Choices and Consequences ; Diffusion Processes; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O38 - Government Policy

References

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