Journal of Credit Risk

Ashish Dev

JPMorgan Chase, New York

In this issue we present three research papers and one technical report.

The first research paper, "Credit default swap trees", is by Ridha Mahfoudhi. This paper deals with the valuation of credit derivatives within the framework of an extended Collin-Dufresne and Goldstein (2001) model. The proposed extension involves replacing a constant long-term target leverage by a time-dependent level. Its main goal is to achieve the flexibility that is necessary for an efficient calibration of the model to market data. First the model is discretized and then the piecewise-constant target leverage function in question is fitted to market quotes of credit default swap spreads. In addition, the fine tuning of the discretized version of the model also requires some adjustment of the recovery rate, making it time-varying, but this effect is secondary. The paper is an interesting attempt to produce a model in which both equity derivatives and credit default swap derivatives can be handled simultaneously.

The second research paper, “Simulation and estimation of loss given default”, is by Stefan Hlawatsch and Sebastian Ostrowski. In this paper, the authors develop an estimation model for loss given default that incorporates the bimodality and the bounded nature of the distribution. To do so, they introduce an adjusted expectation-maximization algorithm to estimate the parameters of a univariate mixture distribution consisting of two beta distributions. They go on to describe numerical experiments on simulated data sets consisting of synthesized loan portfolios each composed of 10 000 obligors. They conclude, based on mean absolute deviations and Q–Q plots, that their model outperforms the benchmark models. The paper provides a loss given default estimation method that is flexible enough to conform to obvious stylized facts (the bimodality and bounded nature of the distribution) present in the data.

The third research paper, “Partial differential equation representations of options with bilateral counterparty risk and funding costs”, by Christoph Burgard and Mats Kjaer, is about pricing derivatives in the presence of counterparty credit risk and funding costs. This topic has gained prominence recently as discount rates for collateralized and noncollateralized derivatives have begun to vary significantly, especially during the recent credit crises. The authors derive general partial differential equations (in some ways extending the work of Black and Scholes) that allow them to compare different funding cases in a consistent framework. They also derive results for the bilateral credit valuation adjustment by extending the standard credit valuation adjustments by taking all funding costs associated with the hedging strategy into account. Since the seller’s funding costs and own credit are intimately related, this results in a consistent treatment of bilateral credit and funding costs in the bilateral credit valuation adjustment calculation. Through examples the authors show that funding costs can have a significant impact.

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 duplication of efforts. The contents of technical reports complement rigorous conceptual and model developments presented in the research papers and provide a lot of value to practitioners.

The technical report in this issue, “Is credit risk really higher in Islamic banks?”, is by Aniss Boumediene. This paper gives a complete overview of the identification and mitigation of credit risk inherent in several financial instruments of Islamic banks. The methodology for measuring credit risk and the modeling are fairly standard but the strength of the piece lies in the novelty of addressing credit risk in the products of Islamic banks. Many scholars of Islamic economics claim that Islamic banking is a more just financial system. However, the claim is generally not accompanied by either strong empirical fact or rigorous theoretical proof. This paper provides some useful evidence in support of such a claim.

REFERENCES

Collin-Dufresne, P., and Goldstein, R. S. (2001). Do credit spreads reflect stationary leverage ratios? Journal of Finance 56, 1929–1958.