From CreditMetrics to CreditRisk and Back Again

In the short time since their public releases in 1997, J.P. Morgan's CreditMetrics and Credit Suisse's CreditRisk have become in uential benchmarks for internal credit risk models. Practitioners and policy makers have invested in implementing and exploring each of the models individually, but have made less progress with comparative analyses. Direct comparison of the models is not straightforward, because the two models are presented within rather di erent mathematical frameworks. One is familiar to econometricians as an ordered probit model, the other is based on insurance industry models of event risk. CreditMetrics and CreditRisk may be addressing the same topic, but they appear to speak in di erent languages. This paper develops methods for translating between these two languages. I show how a restricted version of CreditMetrics can be run through the mathematical machinery of CreditRisk, and how CreditRisk can be mapped into a version of CreditMetrics. A series of simulation exercises uses these translation methods to evaluate the robustness of each model to the assumptions of the other, and to isolate the models' most sensitive restrictions. The views expressed herein are my own and do not necessarily re ect those of the Board of Governors or its sta . I am grateful for the helpful comments of Mark Carey and David Jones. Please address correspondence to the author at Division of Research and Statistics, Mail Stop 153, Federal Reserve Board, Washington, DC 20551, USA. Phone: (202)452-3705. Fax: (202)452-5295. Email: [email protected]. In the short time since their public releases in 1997, J.P. Morgan's CreditMetrics and Credit Suisse's CreditRisk have become in uential benchmarks for internal credit risk models. Practitioners and policy makers have invested in implementing and exploring each of the models individually, but have made less progress with comparative analyses. The two models are intended to measure the same risks, but impose di erent restrictions and distributional assumptions, and suggest di erent techniques for calibration. Thus, given the same portfolio of credit exposures, the two models will, in general, yield di ering evaluations of credit risk. Determining which features of the models account for di erences in output would allow us a better understanding of the sensitivity of the models to the particular assumptions they employ. Unfortunately, direct comparison of the models is not straightforward, because the two models are presented within rather di erent mathematical frameworks. The CreditMetrics model of default is familiar to econometricians as an ordered probit model. Credit events are driven by movements in underlying unobserved latent variables. The latent variables are assumed to depend on external \risk factors." Common dependence on the same risk factors gives rise to correlations in credit events across obligors. The CreditRisk model is based instead on insurance industry models of event risk. Instead of a latent variable, each obligor has a default probability. The default probabilities are not constant over time, but rather increase or decrease in response to background macroeconomic factors. To the extent that two obligors are sensitive to the same set of background factors, their default probabilities will move together. These co-movements in probability give rise to correlations in defaults. CreditMetrics and CreditRisk may be addressing the same topic, but they appear to speak in di erent languages. The purpose of this paper is to show how to translate between these two languages. Section 1 shows how a restricted version of CreditMetrics can be run through the mathematical machinery of CreditRisk. Section 2 maps CreditRisk into a version of CreditMetrics. Section 3 (not