This issue of The Journal of Risk Model Validation focuses rather heavily on capital requirements; indeed, three of the four papers provide analyses of capital requirements, albeit taking different approaches. If we treat Solvency II as “Basel for Insurers”, then Basel is the driving factor in all three cases. Our fourth paper is completely different, however, in that it provides analytic formulas for a class of distributions; a valuable contribution, no doubt, but with quite a different motivation.
While Basel I through Basel III have all suffered criticism to varying degrees, it is clear that one positive by-product of their problematic history is better risk research. This is similar to when NASA’s space project expenditure led to the – initially unintentional – creation of the technology now embedded in smartphone cameras. Whether the world is better off due to the presence of smartphone cameras is debatable, but I have no doubt that the world has been improved by better risk research.
“Procyclicality of capital and portfolio segmentation in the advanced internal ratings-based framework: an application to mortgage portfolios” by José J. Canals-Cerdá is the first paper in this issue. In it, the author investigates the procyclicality of capital in the advanced internal ratings-based (A-IRB) Basel approach for retail portfolios and identifies the fundamental assumptions required for stable A-IRB risk weights over the economic cycle. Canals-Cerdá distinguishes between cyclical and acyclical segmentation risk factors and, through application to a portfolio of first mortgages, shows that risk weights remain stable over the economic cycle when the segmentation scheme is derived using acyclical factors, while segmentation schemes that include cyclical risk factors are highly procyclical. The above description is almost verbatim from the abstract and, written in such terms, the paper’s aim may sound simple; however, the author uses this analysis to highlight important limitations of the A-IRB framework and the implicit restrictions embedded in recent regulatory guidance that underscore the importance of rating systems that remain stable over time and throughout business cycles. It seems to me like this will be fundamentally important to readers who maintain or build risk models in this regulatory environment.
Our second paper, “Optimal allocation of model risk appetite and validation threshold in the Solvency II framework” by Liyi Lin, Marc Heemskerk and Peter Dekker, looks at the Solvency II requirement that stipulates that insurers must either use the European Insurance and Occupational Pensions Authority’s standard formula or develop an internal model to calculate a solvency capital requirement (SCR). The authors propose a structure to help address the currently unavoidable errors involved in such calculations: they employ a validation threshold as a function of the acceptable error in the final metric (top-level SCR) used for final decision making. Together with the concept of model risk appetite, they construct an optimization framework for validation with the potential for application to a wide range of validation problems.
The issue’s third paper is “A risk-sensitive approach for stressed transition probability matrixes” by Ahmet Perilioglu, Karina Perilioglu and Sukriye Tuysuz, who provide a simulation-based methodology for the estimation of stressed through-the-cycle transition probabilities in order to provide a practical technique in stress testing. The output used to capture the impact of the stress test is the transition probability matrix. The benefit of the simulation-based approach can be seen in its ability to capture nonstationary phenomenons, such as time-varying correlations, which are more likely to reflect economic phenomenons.
Our fourth and final paper is by José María Sarabia and Enrique Calderín-Ojeda and is titled “Analytical expressions of risk quantities for composite models”. This is quite different from the previous three papers, being as it is concerned with the statistical derivation of quantiles and other distributional measures for models based on the McDonald’s family of probability distributions. This is a family that generalizes many of the well-known distributions in risk theory, and it is a useful tool in providing fairly general analytical results. Applications of the model are in the area of insurance.
Trinity College, University of Cambridge
Procyclicality of capital and portfolio segmentation in the advanced internal ratings-based framework: an application to mortgage portfolios
This paper investigates the procyclicality of capital in the advanced internal ratings based (A-IRB) Basel approach for retail portfolios, and identifies the fundamental assumptions required for stable A-IRB risk weights over the economic cycle.
In this paper, the authors derive an analytical solution for sub-SCR VTs starting with a model risk appetite (MRA) that defines acceptable errors for an insurer’s total SCR.
In this paper, the authors outline a simulation-based methodology for the generation of stressed transition probability matrixes under the structural credit risk framework.
In this paper, the authors obtain analytic expressions of different actuarial and statistical quantities for a general class of composite models derived from the McDonald’s family of probability distributions.