Journal of Risk Model Validation

Steve Satchell
Trinity College, University of Cambridge

We live in a time when the phrase “supply-chain problems” is ubiquitous. Readers may think of this as having to do with supermarkets or fuel supplies, but supplychain problems have also engulfed The Journal of Risk Model Validation. We only have three articles in this issue; fortunately, they are all of a high quality.

Our first paper, “A prudent loss given default estimation for mortgages. II” by Bogie Ozdemir and Emma Huang, addresses mortgage book risk. At least in the United Kingdom, mortgage book risk has been very low recently, but there are a number of reasons why this will likely change. The focus of this paper is on providing an accurate estimate of loss given default (LGD) for mortgage portfolios and on having the ability to stress test these portfolios effectively. Ozdemir and Huang introduce a prudent methodology for doing so. Their methodology builds on their earlier work, which provides an accurate estimation of “workout” LGD by directly modeling the house value at default by incorporating market effects and potential appraisal biases. To improve on it, in this extension, the probability of “curing” and the probability of full payment after default (“exit”) are explicitly modeled with respect to the inverse of the loan-to-value ratio. This makes the LGD estimation more accurate and risk sensitive, and makes it particularly suitable for stress testing purposes. While the methodology is presented in a mortgage setting, it has applications to all types of secured lending where the collateral value relative to the loan size will likely influence the potential outcomes following the default. Clearly, this is quite broad.

In the issue’s second paper, titled “Evaluation of backtesting techniques on risk models with different horizons”, Grigorios Kontaxis and Ioannis E. Tsolas investigate the impact of differing the time horizon on value-at-risk (VaR). The authors inspect different models of volatility and returns as well as different backtesting techniques and time horizons. Unsurprisingly, they find no uniform model, concluding that:

For short horizons, some approaches underestimate VaR. However, various models present violation estimates that almost converge to the desired ones, according to the confidence levels used. Further, nonoverlapping returns tend to yield satisfactory results for most models. The main conclusion of this study is that the horizon selection can affect the estimation, and consequently the backtesting, of VaR models in some cases.

In some sense, there are no new revelations in their results, but readers will find it helpful if they are currently using some of the models in the study to look up some model-specific details.

The final paper in the issue is “Calibration of rating grades to point-in-time and through-the-cycle levels of probability of default” by Mark Rubtsov. This paper proposes an integrated scheme linking point-in-time (PIT) and through-the-cycle (TTC) measures of probability of default (PD). Rubtsov states the importance of “dual calibration of a probability of default model”. In his words:

It explains why such a calibration should happen at the rating grade level, and how PD estimates can be assigned to a bank’s existing rating grades, ie, without introducing any changes to either the underlying (hybrid) rating function or the rating scale. This is done by first translating the traditional asymptotic single risk factor model underlying the Basel risk-weight formulas from its original obligor level to the rating grade level, and then determining the model’s parameters by using a maximum likelihood estimation. Standard deviations of the estimates obtained then provide a link to the regulatory margin of conservatism. Rating migration adds a new dimension to the model and leads to procyclical deviations of TTC PDs per grade from their long-term average counterparts. A link between rating migration and calibration levels gives a new definition to the rating function’s degree of PIT-ness, which becomes a key parameter responsible for the TTC stability at the portfolio level. The closed-form solutions obtained are flexible with respect to different patterns of rating migration and explicitly account for a prediction error in the business cycle model. The proposed technique is illustrated on a sample of corporate customers.

The paper strikes me as an excellent mix of academic rigor and useful practical relevance.

Overall, I hope readers will value this issue, where the emphasis is on quality rather than quantity. Apparently, such a change has a history in theories of social evolution usually attributed to Hegel – perhaps, though, making such an editorial claim might be a little grandiose.