Journal of Credit Risk

Michael K. Ong

Stuart Graduate School of Business, Illinois Institute of Technology

I welcome you to the final issue of The Journal of Credit Risk under my editorship. Due to increasing workload, I shall be stepping down as Editor-in-Chief after this issue although I shall continue to serve as a member of the editorial board. I would like to take this opportunity to thank all of you for your great support and guidance during the inaugural year of the Journal.

It has been a great joy for me to oversee its successful launch and to manage its transition into a very well respected publication during its first year. The journal continues to receive very positive reactions from the public. Now that its continued success is assured, I am very pleased to hand it over to very capable hands.

As I have said many times before, this journal is your venue for communicating results in the modeling and management of portfolio credit risk, and in the pricing and hedging of credit derivatives – in particular, structured credit products and securitizations. Please continue to contribute to the four different sections of the journal. More specifically, I would like to highlight the opportunity for you to share your insights, thoughts, queries and solutions to practical problems in the Forum and Problems and Solutions sections. Please continue to use these to discuss current issues in the field.

Research Papers

There are five full-length research papers in the main section. Incorporating the mark-tomarket facet of counterparty risk introduces a major computational complication when dealing with non-linear products. The first paper, by Stuart Turnbull, entitled “The pricing implications of counterparty risk for non-linear credit products”, draws upon a recent work by Marshall and Naldi (2005) and extends their analysis to derive upper and lower bounds for the misspecification in the P&L and examine the tightness of the upper and lower bounds. The extended methodology proposed in the paper provides practitioners and regulators with a practical tool for the determination of reserves to incorporate the two facets of counterparty risk: failure to perform, and mark-to-market exposure. The paper further shows that, for many applications, the bounds are tight and the creditworthiness of counterparties can have a major impact on the P&L.

The second paper, “Linear and non-linear credit scoring by combining logistic regression and support vector machines” by T. Van Gestel, B. Baesens, P. Van Dijcke, J. A. K. Suykens, J. Garcia and T. Alderweireld, addresses a very important aspect of the internal risk rating system requirement of the Basel II capital accord. The authors propose some enhancements to credit scoring techniques given its importance in bank risk management. They combine linear and kernel-based learning techniques (support vector machines) to achieve a model with a high level of readability and discrimination power. As a test case the authors apply the enhanced techniques to an internal rating model for banks.

In the third paper, “Credit portfolio risk and probability of default confidence sets through the business cycle”, Stefan Trück and Svetlozar Rachev investigate the effect of different migration behavior through the business cycle on capital requirements for an illustrative loan portfolio. They investigate the effect of changes in migration matrices on credit portfolio risk in terms of expected loss and value-at-risk, and they determine tight confidence intervals for investment grade rating classes. The authors discover that the variations in width and level of confidence intervals are significant, and further find a decreasing coefficient of variation for PD confidence sets with increasing riskiness of the loan. They conclude that using average transition matrices might not be suitable as input for rating-based credit risk modeling.

Continuing with the same Basel II theme, the fourth paper, by Peter Miu and Bogie Ozdemir, entitled “Practical and theoretical challenges in validating Basel parameters”, discusses the validation exercise experience of a Canadian bank in its preparatory work for Basel II. In light of the current debate on a consistent rating system philosophy (point-in-time (PIT) versus through-the-cycle (TTC)), the authors argue that not only PD itself but the correlation of PD used in economic capital models should be rating systemspecific. They conclude that one needs to use a larger PD correlation under a TTC rating system than under a PIT rating system. The authors also discuss the inconsistency in the treatment of the distribution of the economic value of LGD at the risk horizon.

Classical structural models of a firm’s equity and debt are based on the assumption that the price of claims on the firm’s assets depends solely and uniquely on a set of underlying state variables, such as the market value of the firm’s assets, as well as claim-specific features such as maturity, callability, etc. The fifth and final paper, by Jorge Sobehart and Sean C. Keenan, entitled “Capital structure arbitrage and market timing under uncertainty and trading noise”, presentsan alternative model based on the notion that participants in the equity and debt markets may disagree on their valuation methodology, introducing uncertainty in the price of claims on the firm’s assets in addition to the uncertainty generated by changes in the assets. The authors show that the introduction of trading noise in the equity and debt markets interferes with arbitrage and hedging strategies and can create potential capital structure arbitrage opportunities.

Credit Risk Forum

There are two discussion articles in the Credit Risk Forum section. How should default probability curves be constructed from market information, and what are the different methods to do this? In his contribution entitled “Bootstrapping default probability curves”, Lawrence Luo explains three common methods for bootstrapping default probability curves from par credit default swap spreads. The first is based on the assumption that the default densities between consecutive CDS maturities of given CDSs are constant. The second is based on the assumption that default intensities between consecutive CDS maturities are constant. The third is based on the assumption that CDS spreads of any given maturity can be interpolated from the given CDS spread curve. The two methods that are not based on the assumption of default intensities give back the par CDS spread when the derived default probability curve is used to value the original CDS. The method that is based on the assumption of default intensities also gives back the CDS spread approximately. Numerical results show that when the time gaps between the consecutive maturities of the given CDSs are not too large, the three methods give close results.

However, if such gaps are very large the differences can be significant. In spite of major developments in the collateralized debt obligations (CDO) market, a coherent measure of correlation for comparing prices among different tranches is still wanting. What are base correlations, and what is their role in the relative valuation of CDO tranches? How do base correlations behave under changing behavior of default correlations? Are there potential problems in using base correlations as a quotation device and a relative valuation too? In the second discussion paper, “An evaluation of the base correlation framework for synthetic CDOs”, Søren Willemann uses a simple intensitybased credit risk model to generate tranche spreads and examine the behavior of the base correlations and the merits of the relative valuation approach. His results can be summarized in three points. First, even if tranche spreads from a theoretical model change to reflect an increased default correlation, the base correlations for some tranches can decrease. This implies that if spreads in the market change so as to reflect an increased default correlation, the base correlations may wrongfully indicate that correlations have decreased. Second, relative spread errors can be very large, particularly in the mezzanine tranches, with the errors changing sign from tranche to tranche. Third, base correlations are only unique given the set of attachment points. This means that, across different markets, base correlations will be different simply because the structure of traded tranches is not the same.

Problems and Solutions

The Problems and Solutions section is intended to encourage active discussion on how some of the many interesting questions and issues surrounding credit risk can be solved. The section is intended to allow readers to post serious, practical questions or to post previously unknown and novel solutions to difficult questions.

We have a practical question for this issue that seeking solutions and discussions. The discussions will appear in the next issue.

Laurie Donaldson
Managing Editor, Risk Books and Journals

I am very pleased to welcome you to this issue of The Journal of Credit Risk. I am also delighted to say that we have another great line up of important papers from top academics and practitioners operating in the credit risk arena.

I wanted to take this opportunity to announce the departure of Professor Michael Ong as Editor-in-Chief of the journal. After successfully launching the journal, and helping to develop it in a short space of time into one of the most respected and authoritative publications in this field, Michael has decided to move on due to his other commitments. His successor as Editor-in-Chief will be announced shortly.

I would like to thank Michael for the guidance and editorial rigor that has characterized his leadership of the journal. On behalf of the Editorial Board and our readers, I would like to express my appreciation for all his work in helping create such an esteemed and innovative forum for your research.