This fall issue of The Journal of Risk Model Validation brings together three papers with a credit focus and one paper that is a more general methodological piece. This latter paper is likely to resonate more with equity risk managers but all four make useful contributions to risk model validation.
The first paper, titled "A methodology for point-in-time-through-the-cycle probability of default decomposition in risk classification systems" by Magnus Carlehed and Alexander Petrov, uses a Merton model framework (consistent with Basel II formulae) to develop a methodology for point in-time (PIT) and through-the-cycle (TTC) probability of default (PD) estimation in credit risk classification systems, primarily for corporates. The authors claim that such a methodology is important for reducing procyclicality of the capital requirement. The authors mathematically define "degree of point in time" of a rating model and "state of the economic cycle". Simple analytical expressions for full PIT PD and TTC PD are derived, which allow easy implementation of the methodology in a bank's IT system. They further discuss different methods for estimation of parameters as well as possible implications for risk-adjusted profitability and steering. The clarification of such important ideas seems to me to be very useful as they are often bandied about in a rather loose manner among practitioners.
The second paper in the issue, "Does using time-varying target leverage ratios in structural credit risk models improve their accuracy?", is by Cho-Hoi Hui, Tak-Chuen Wong, Chi-Fai Lo and Ming-Xi Huang. In it the authors assert that empirical findings and theoretical studies suggest that firms adjust toward time-varying target leverage ratios. The paper studies the performances of the default probabilities generated from two structural credit risk models with time-dependent and constant target leverage ratios, respectively, and credit ratings. The time-dependent model consistently performs better than the other model and credit ratings in terms of discriminatory power of differentiating firms' default risk and capability for predicting default rates over the period 1996-2006. The material differences between the predictive capability of the two models show that the time dependency of the target leverage ratio is a critical factor in modeling credit risk. The study also provides evidence to support the existence of a time-varying target leverage ratio.
The issue's third paper, "Empirically testing for the location-scale condition: a review of the economic literature" by Michael Vassalos, Carl R. Dillon and Paul D. Childs, explores the link between two major theories of economic decisions under uncertainty: mean-variance and expected utility. The authors focus on a condition that means that the former is consistent with the latter: namely, the location-scale (LS) condition. In particular, if one can verify the LS condition, there is a clear sense in which a mean-variance approach, which assumes a portfolio variance as the risk measure, will be validated. This paper reviews the economic literature related to empirically testing for the LS condition, discusses the advantages as well as the limitations of those techniques and examines alternative ways of testing for the LS condition that are used mainly in the statistics literature.
While many practitioners rarely challenge the theoretical underpinnings of their risk models, such an activity can often reveal why a model's performance is so poor.
The fourth paper in this issue, "Modeling issuer default risk in basket default swaps: the impact of default correlation" by Po-ChengWu, investigates the hedging performance of basket default swaps (BDSs), which is a commonly traded instrument for the hedging and investment of a credit portfolio.A one-factor copula model is the most popular model for credit derivative pricing. However, when considering the issuer default risk, this model may fail to measure the effect of the issuer default risk on BDSs. This article discusses the bias that may be present in the pricing of a vulnerable BDS under the one-factor copula model, and also constructs a multifactor copula framework to show how issuer default risk affects BDS rate. The results of this research reveal that the issuer default risk might affect the fair BDS rate significantly. To appraise the risk of a vulnerable BDS, the author argues that the default correlation between issuer and reference entities must be considered in the model.
It is interesting to note that a large proportion of the authors in this issue are associated with Asian-based employers. This is a most welcome development and may reflect two things. One is the ever increasing importance of Asian markets in the global financial system. The second is the real possibility that Asian markets are simply better organized and regulated and this is reflected by a greater awareness of model validation.