A Comparative Analysis of Current Credit Risk

A comparative analysis of current credit risk models q Michel Crouhy a, * , Dan Galai b , Robert Mark a a Canadian Imperial Bank of Commerce, Market Risk Management, 161 Bay Street, Toronto, Ont., Canada M5J 2S8 b Hebrew University, Jerusalem, Israel Abstract The new BIS 1998 capital requirements for market risks allows banks to use internal models to assess regulatory capital related to both general market risk and credit risk for their trading book. This paper reviews the current proposed industry sponsored Credit Value-at-Risk methodologies. First, the credit migration approach, as proposed by JP Morgan with CreditMetrics, is based on the probability of moving from one credit quality to another, including default, within a given time horizon. Second,

the option pricing, or structural approach, as initiated by KMV and which is based on the asset value model originally proposed by Merton (Merton, R., 1974. Journal of Finance 28, 449–470). In this model the default process is endogenous, and relates to the capital structure of the firm. Default occurs when the value of the firm s assets falls below some critical level. Third, the actuarial approach as proposed by Credit Suisse Financial Products (CSFP) with CreditRisk+ and which only focuses on default. Default for individual bonds or loans is assumed to follow an exogenous Poisson process. Finally, McKinsey proposes CreditPortfolioView which is a discrete time multi-period model where default probabilities are conditional on the macro-variables like unemployment, the level of interest rates, the growth rate in the economy, ... which to a large extent drive the credit cycle in the economy. 2000 Elsevier Science B.V. All rights reserved. JEL classification: G21; G28; G13 Journal of Banking & Finance 24 (2000) 59–117 www.elsevier.com/locate/econbase q This work was partially supported by the Zagagi Center. * Corresponding author. Tel.: +1-416-594-7380; fax: +1-416-594-8528. E-mail address: crouhy@cibc.ca (M. Crouhy). 0378-4266/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 4266(99)00053-9 Keywords: Risk management; Credit risk; Default risk; Migration risk; Spread risk; Regulatory capital; Banking 1. Introduction BIS 1998 is now in place, with internal models for market risk, both general and specific risk, implemented at the major G-10 banks, and used every day to report regulatory capital for the trading book. The next step for these banks is to develop a VaR framework for credit risk. The current BIS requirements for ‘‘specific risk’’ are quite loose, and subject to broad interpretation. To qualify as an internal model for specific risk, the regulator should be convinced that ‘‘concentration risk’’, ‘‘spread risk’’, ‘‘downgrade risk’’ and ‘‘default risk’’ are appropriately captured, the exact meaning of ‘‘appropriately’’ being left to the appreciation of both the bank and the regulator. The capital charge for specific risk is then the product of a multiplier, whose minimum volume has been currently set to 4, times the sum of the VaR at the 99% confidence level for spread risk, downgrade risk and default risk over a 10-day horizon. There are several issues with this piecemeal approach to credit risk. First, spread risk is related to both market risk and credit risk. Spreads fluctuate...

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