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February 2010

Research Results

A working paper by Prof. Jin-Chuan Duan, Director of NUS Risk Management Institute and Cycle & Carriage Professor of Finance, NUS Business School.

Prof. Jin-Chuan Duan has just finished his new working paper "Clustered Defaults" in which he built a hierarchical intensity model to analyze defaults of firms in one or many economies. The model is also useful for dealing with many obligors in a large credit portfolio.

Credit risk analysis of large portfolios is at the heart of credit risk management, and understanding clustered defaults in an economy has important regulatory policy implications. Credit rating agencies, however, have been severely criticized for not fulfilling their responsibility in revealing obligors' credit risk, with the models used by such agencies seriously questioned in the light of the current crisis.

As part of the remedial solutions, better credit analytical tools for modeling a large pool of obligors are needed. In academic literature, one popular approach is the Poisson intensity model. The key feature of such model is the ability to proxy the obligor's credit risk through the obligor's default intensity. With it, a modeler can calculate the intensity as a function of macroeconomic variables as well as firm-specific variables. However, the traditional Poisson intensity model has been shown to be incapable of capturing the clustering feature of defaults. The joint default probability of more than one obligor implied by these models is too low to fit the observed default patterns.

In order to capture the bursting defaults" phenomena, the paper develops a hierarchical intensity model with three layers of shocks. In the hierarchical intensity model, a company might default due to three different types of shocks: common shocks (macro-economic shocks), group-specific shocks (industry-wide shocks) and individual shocks. A common shock would affect all the obligors in the portfolio while a group-specific shock only has influence on the obligors in a specific group. The hierarchical intensity model differs from the traditional Poisson intensity model mainly due to its common and group-specific shock components. It is these two components that lead to higher joint default probabilities and higher default correlations.

Therefore, the hierarchical intensity model can better capture clustered defaults. Quite importantly, the hierarchical intensity model can be implemented by adopting the maximum likelihood estimation method.

By examining the U.S. corporate default and bankruptcy data from 1991 to 2008, the paper compares the hierarchical intensity model with a traditional intensity model. The variables used to construct different intensities included firms' trailing one-year return, a volatility adjusted leverage measure called distance to default, three-month Treasury bill rate, trailing one-year S&P 500 index returns and average distance to default. Unlike most papers in the literature, the author also included financial firms in the data.

Accordingly, distance to default was calculated by taking a firm's other liabilities into consideration because a financial company might have significant liabilities that are classified as neither short-term debt nor long-term debt.

The empirical results show that hierarchical intensity model performs much better than the traditional intensity model. The likelihood ratio test result suggests the existence of common shocks. To show the difference between the hierarchical intensity model and traditional intensity model, the author also devised the so-called signature plot by averaging the predicted default distributions over time. Such plots can be compared with the observed default frequency. By employing such a method, the difference between the two models is quite evident.

The paper also provides the Kullback-Leibler distance of the two default distributions implied by two different models. The time series of Kullback-Leibler distance indicate that the two predicted default distributions differ more when average distance to default is either extremely high or extremely low.

In summary, this paper proposes a new hierarchical intensity modeling approach to handling clustered defaults. The performance of such model has been shown to be superior to the traditional intensity model using the U.S. default and bankruptcy data in the past two decades.

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Published quarterly by Risk Management Institute, NUS
Editor: Ivy Wang (rmiwy@nus.edu.sg)