Kilian Plank

Correlation Smile, Volatility Skew and Systematic Risk Sensitivity of Tranches.

In collateralized debt obligations and other securitized credit derivatives, the expected tranche payoffs depend heavily on the default correlations among the securities in the pool. Like volatility, correlation is not directly observable, but it is possible to infer it from the market price of a tranche. But unfortunately, also like volatility, these implied correlations don’t behave well. They should be equal across all of the tranches created from a given pool, but they never are. Instead, implied correlations exhibit the pattern known as correlation skew. In this article, Hamerle, Igl, and Plank consider two ways in which the real world departs from the assumptions of the Gaussian copula model. Different correlations extracted from different tranches is one, but the other departure is that investors require expected risk premia for bearing a security’s downside exposure. This is not the same as a (symmetrical) distaste for “volatility,” say, and it is reflected in an asymmetrical implied volatility skew exhibited by options on a bond issuer”s equity. The standard Gaussian copula model allows for the first effect, but not the second. In this article, the authors look at both. Their most successful model estimates downside risk premia from the risk-neutral probability densities extracted from the issuers’ equity options and then imposes a fixed and moderate degree of correlation. This combination captures market pricing very well for all of the tranches above the equity tranche.

Stress-testing CDOs

Analyses regarding the responsibility of risk management for the current credit crisis have found a lack of stress tests as one important issue. In this article, we argue that stress tests are an even more important risk management tool with structured finance products such as collateralized debt obligations. We explain why the specific risk profile of such assets requires dynamic modeling. In an extensive case study, a stress-test comparison is made between portfolios including conventional bonds and structured products. The results clearly show the increased risk contribution of structured products which can only be revealed explicitly in a dynamic view.

Diversification Potential of Structured Securities

Diversification has been a frequently stated benefit of structured securitizations. In the subprime crisis, however, CDOs (especially ABS CDOs) proved to be concentrations of risk. In this article, the author examines different diversification patterns of structured securities that were deemed beneficial by investors and finds that name diversification is largely ineffective and may even increase the risk of tranches. Similarly, factor or sector diversification in the pool may not have the anticipated effect. Positive effects are only achievable for senior tranches, and for mezzanine tranches, the risks may even increase. These results shed new light on the diversification potential of CDOs, which is important in terms of both risk management and valuation.

A note on the Berkowitz test with discrete distributions

Berkowitz (2001) suggested a powerful and popular density test based on a probability integral transformation (PIT). For the PIT to work properly the original distribution needs to be continuous. In this article, we show what problems can arise when the procedure is applied to discrete distributions. We suggest a simple modification so that the basic assumptions of the Berkowitz test are recovered.

Stress Tests of Credit Risks

The last credit and financial crisis has rendered credit risk stress tests a major risk management topic for financial authorities and banks. However, implementing a reasonable stress test with useful results is still considered as difficult and this in turn implies problems of acceptance in the financial industry. One reason for these difficulties seems to be the many degrees of freedom associated with the selection of scenarios. Another reason may be that no “best practice” guidelines do exist. This article gives a survey on credit risk stress tests. We want to clarify important terms and set a formal foundation. Furthermore, we want to distinguish different types of stress tests, their objectives, strengths and weaknesses and explain different methodologies.

Integration of Structured Finance Exposures in theBasel II Model:Analytical Results

For efficiency reasons or because of a lack of detailed data, financial institutions frequently treat structured finance securities similar to conventional fixed-income products such as bonds or loans, which are characterized by rating, correlation, and loss-given default. Structured finance securities, however, have a specific risk profile. They tend to concentrate losses in adverse states of the systematic risk factor. This fact implies that simply adopting risk parameters of conventional bonds or loans is an inappropriate technique. The author shows that, under the Basel II framework, tranches have to be modeled with an increased factor loading. They derive an analytical calibration procedure for the Basel II model that appropriately captures the risk profile of tranches. This finding not only allows for seamless integration of structured and conventional exposures in a portfolio model, but also offers insights into the concentration effects of tranches.

Copula Choice with Factor Credit Portfolio Models

Over the last couple of years we could observe a strong growth of copula based credit portfolio models. So far the major interest has revolved the ability of certain copula families to map specific phenomena such as default clustering or the evolution of prices (e.g., credit derivatives prices). Still few questions have been posed regarding copula selection. This is surprising as the problem of estimating the dependence structure is even unresolved with simple traditional models. For statistical tests of credit portfolio models in general the literature found densitybased tests like that of Berkowitz (2001) the most reasonable option. In this text, we examine its power characteristics concerning factor portfolio models in more detail. Our results suggest that both the copula family as well as the level of dependence is generally very difficult to identify.

Intransparenzen auf Verbriefungsmärkten

ZusammenfassungDie im Jahr 2007 aufkommende Finanzkrise nahm ihren Ursprung in dem über viele Jahre hinweg boomenden Verbriefungsmarkt. Mitverantwortlich für das enorme Ausmaß der entstandenen Verluste waren Informationsdefizite beziehungsweise Informationsasymmetrien zwischen verschiedenen Marktteilnehmern, die bei strukturierten Produkten wie Asset Backed Securities (ABSs) oder Collateralized Debt Obligations (CDOs) eine besondere Hebelwirkung entfalten. Der vorliegende Beitrag erklärt die erhöhte Sensitivität der Ratings beziehungsweise Bewertungen von ABSs und CDOs in Bezug auf fehlerhafte Eingangsdaten oder Fehlkalibrierungen. Als wesentliche Schlussfolgerung ergibt sich die Notwendigkeit einer effektiveren Informationsversorgung entlang der gesamten Verbriefungskette.