Journal of Credit Risk

Ashish Dev

JPMorgan Chase, New York

In this issue we present three full-length research papers and two technical reports. The first research paper, "A credit default model for a dynamically changing economy", is by Patrik Andersson. In this paper Andersson proposes a simple model of the default process by drawing upon research into the spread of disease among humans.

By incorporating default contagion into the model, the author reproduces the cyclicality of default intensities that are empirically observed in the economy without explicitly introducing any external macroeconomic factors. A recession is characterized as a cleansing of the unhealthy companies during the recession, and the recession ends when a sufficient number of the unhealthy companies have left the economy. In the model, this results in oscillations representing business cycles. A sensitivity analysis of the contagion parameter shows that the model predicts that tighter connections in the economy will result in faster oscillations of the default process.

The second research paper, “Modeling sector correlations with CreditRiskC: the common background vector model”, is by Matthias Fischer and Christian Dietz. In this paper the authors describe a quantitative approach that allows parameters to be fitted to the different types of risk factor correlation structures. A simple analytical model is introduced to take sector correlations into account within the CreditRiskC framework. The dependence between the sector variables is introduced with several (additive) background factors (“background vectors”). The paper generalizes thework of Han and Chang (2008) and provides a better match to an externally given correlation matrix of the risk factors. This is achieved by minimizing the differences between observed and theoretical (implicit in the model) covariance matrices.

The third research paper, “Generalized beta regression models for random loss given default”, is by Xinzheng Huang and Cornelis Oosterlee. The authors describe a framework for using generalized beta regression (GBR) for systematic loss given default (LGD). The GBR framework generalizes the beta regression model proposed by Ferrari and Cribari-Neto (2004) and provides considerable flexibility for random LGD modeling, accommodating skewness and heteroskedastic errors well. Three types of GBR models (one basic model and two extensions) are introduced using parameter estimation methods and an example of calibration. The authors then go on to show that the models can be easily combined with normal approximations or saddlepoint methods to calculate value-at-risk or expected shortfall for any portfolio loss distribution.

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 first technical report, “Market pricing of credit-linked notes: the case of retail structured products in Germany”, is by Andreas Rathgeber andYunWang. This paper presents an empirical study of the pricing of credit-linked notes in the primary market in Germany. The authors include all 136 credit-linked notes issued between 2005 and 2009 in Germany. The German market is one of the most important markets for such notes. For single reference entities (firms or countries), the authors derive (risk-neutral) probabilities of default from spreads of credit default swaps. When there are multiple reference units, the dependence structure of defaults must also to be taken into account. In these cases, the authors assume a single-factor Mertontype model with multivariate normal returns of the underlying assets.A firm defaults when its asset value falls below a certain threshold. This threshold is estimated such that it is consistent with the observed credit default swap spread. The results support the hypothesis that the products are overpriced compared with theoretical fair values. This finding is robust with respect to different specifications of the unknown variables (especially the recovery rate). The authors show that a significant part of the crosssectional variation of overpricing levels can be explained by specific determinants that are justified on intuitive grounds.

The second technical report, “Approximating independent loss distributions with an adjusted binomial distribution”, is by Dominic O’Kane. The paper provides a new recursion with which to (approximately) derive the loss distribution of a credit portfolio using a simple adjustment of the binomial distribution. The approximation is heuristic in nature. Such techniques are typically used when obligors are assumed to be conditionally independent or conditionally independent and identically distributed after having conditioned on the common factor(s). The algorithm can handle both homogeneous and inhomogeneous loss portfolios and is a fast and accurate alternative to the exact recursion approach. The author compares the adjusted binomial algorithm with other loss distribution approximation algorithms in the context of pricing index tranches and shows that the technique works quite well in the cases studied.

REFERENCES

Han, C., and Kang, J. (2008). An extended CreditRiskC framework for portfolio credit risk management. The Journal of Credit Risk 4(4), 63–80.

Ferrari, S., and Cribari-Neto, F. (2004). Beta regression for modeling rates and proportions. Journal of Applied Statistics 31, 799–815.

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