Journal of Credit Risk

In this issue of The Journal of Credit Risk we present two research papers and two technical reports.

The first research paper is "Recursive formulas for the default probability distribution with applications in Markov chain-based intensity models" by Daniel W.-C. Miao and Ben M. Hambly. The paper looks at the probability distribution of the number of defaults in pricing problems of multiple-name credit derivatives. The authors derive a recursive formula that is useful for the calculation of such a default distribution and prove that the formula holds. They then extend the results to the case of heterogeneous groups, although the usefulness of the proposed formula is limited by its high computational complexity. The recursive formulas are extended further to some new versions that allow for multiple heterogeneous subgroups of homogeneous entities.

The second research paper in the issue, "An asset drop model as an alternative to the treatment of double defaults within the Basel framework", is by Sebastian Ebert and Eva Lütkebohmert. In this paper the authors address the problem of estimating economic capital for exposure guarantees with a focus on regulatory applications. The authors present an "asset drop" model as an alternative to the treatment of double default in Basel II. In contrast to the Basel II treatment, defaults of the obligor and of the guarantor are treated as independent, conditional on the systematic factor. Instead of introducing a "local" systematic risk factor that relates obligor and guarantor, the probability of default of the guarantor is adjusted upward. To calculate the probability of default adjustment, the asset drop model calculates the default threshold implied by the guarantor's probability of default, increases the threshold by the amount of the guarantee, and recalculates the probability of default using the new threshold. The model presented by the authors has several advantages over the model underlying the Basel II double default treatment. One of these advantages is that the obligor and guarantor are not treated symmetrically: default of the obligor increases the probability of default of the guarantor, but default of the guarantor has no effect on the obligor.

A technical report describes a particular practical technique and enumerates situations in which it works well and others in which it does not. Such reports provide extremely useful information to practitioners in terms of saved time and minimizing duplication of effort. The contents of technical reports complement rigorous conceptual and model developments presented in the research papers. A technical report can be a useful survey article as well.

The first technical report in this issue is "A survey of loan credit default swap pricing models" by Michael Ong, Dan Li andDavid Lu. It is a survey of pricing models for loan credit default swaps (LCDSs). The authors review several prevailing LCDS pricing approaches. The LCDS is a relatively new financial product and its modeling is yet to be standardized. The article summarizes a range of possible modeling approaches.

The second technical report is "Collateralized credit default swaps and default dependence: implications for the central counterparties" by Masaaki Fujii and Akihiko Takahashi. The authors have studied the pricing of CDSs under the assumption of continuous collateralization and they obtain a simple pricing formula for the collateralized CDS. This is expected to be particularly relevant for the central counterparties dealing with CDSs and other credit-linked products for which the assumption of continuous collateralization is a reasonable proxy of reality.

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