Journal of Risk Model Validation

Steve Satchell
Trinity College, University of Cambridge

Since I have always held the view that the topic of risk model validation is much wider than just the world of credit, and actually applies to all areas of finance, it is especially pleasing to have a paper in this issue that looks at strategies of a fairly general nature. We shall return to that in due course. Again, we have four papers in this issue.

Our first paper is “Comprehensive Capital Analysis and Review consistent yield curve stress testing: from Nelson–Siegel to machine learning”, by Vilen Abramov, Christopher Atchison and Zhengye Bian. Following the financial crisis of 2007–9, the Federal Reserve established a stress testing framework known as the Comprehensive Capital Analysis and Review (CCAR). The regulatory stress scenarios do not define stress values for all relevant risk factors. In particular, only three Treasury rates are captured in these scenarios: the three-month, five-year and ten-year ones. The large financial institutions that are subject to CCAR need to complement CCAR scenarios by defining stress values for the missing risk factors. The authors of this paper investigate CCAR-consistent Treasury yield curve stress testing. I understand this to mean that perturbations from the assumed yield curve need to be consistent with the correlation structure of the various yield series. They consider three modeling approaches that allow us to “build” the stressed curves under CCAR scenarios: Nelson–Siegel, principal components and neural networks. The paper provides the necessary analysis to provide CCAR-consistent Treasury yield curve stress tests.

The issue’s second paper, “The value-at-risk of time-series momentum and contrarian trading strategies” by Keunbae Ahn, Jihye Park and Kihoon Jimmy Hong, not only provides a theoretical model for the value-at-risk (VaR) of active and passive trading strategies, but also has substantial implications relevant to risk management. While it may be argued that this paper is not directly focused on risk model validation, it does consider a much wider class of problems than the papers this journal normally publishes. The authors’ results suggest, first, that passive strategies are riskier than active trading strategies based on historical returns, including the momentum and contrarian strategies; second, that momentum (contrarian) trading is riskier in a bull (bear) market; and third, that the VaR of momentum (contrarian) strategies has a positive relation with the absolute value of the return autocorrelation as well as a positive (negative) relation with the state of the market. Furthermore, the authors show that momentum trading strategies give a risk-adjusted performance superior to other strategies in the international stock markets. The last result I find surprising, but, of course, empirical analysis will always be data and epoch dependent.

Returning to more familiar material, the third paper in this issue, by Mark Rubtsov, is titled “Backtesting of a probability of default model in the point-in-time–throughthe-cycle context”. This presents a backtesting framework for a probability of default (PD) model, assuming that the latter is calibrated to both point-in-time (PIT) and through-the-cycle (TTC) levels. The author claims that the backtesting scope both includes calibration testing (aiming at establishing the unbiasedness of the PIT PD estimator) and measures calibration accuracy, which, according to Rubtsov’s definition, reflects the magnitude of the PD estimation error. He argues that model correctness is equivalent to unbiasedness, while accuracy, being a measure of estimation efficiency, determines model acceptability. He explains how the PIT-based test results may be used to draw conclusions about the associated TTC PDs. Using this framework, Rubtsov finds fault with the popular binomial and chi-squared tests, and he offers alternative tests and confirms their usefulness in Monte Carlo simulations. The framework is further used to provide other analysis that I will not describe here.

Our final paper in this issue is “A pricing model with dynamic credit rating transition matrixes” by Yun-Cheng Tsai, Sheng-Hsuan Lin and Yuh-Dauh Lyuu. This paper discusses modeling and risk validation issues with credit-sensitive notes (CSNs), a product class I must admit I was previously ignorant of. Assuming that my ignorance is shared by others, I should explain that a CSN is a corporate couponbearing bond whose floating coupon rates link to the credit rating of the corporation. Acharya, Das and Sundaram (ADS) have proposed a model for pricing them, but their lattice algorithm runs in exponential time. Furthermore, the ADS model uses a constant credit rating transition matrix, which is a somewhat restrictive assumption. Tsai, Lin and Lyuu incorporate a stochastic credit rating transition matrix into the ADS model and implement a simulation-based pricing method. When applied to CSN pricing, the new approach is more efficient than the lattice algorithm. It also has the property that the stochasticity of the credit rating transition matrix has an impact on the prices, particularly for lower-rated classes.

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