This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable data. This model is useful for pricing and hedging corporate debt with imbedded options, for pricing and hedging OTC derivatives with counterparty risk, for pricing and hedging (foreign) government bonds subject to default risk (e.g., municipal bonds), for pricing and hedging credit derivatives, and for risk management. This article presents a simple model for valuing risky debt that explicitly incorporates a firm's credit rating as an indicator of the likelihood of default. As such, this article presents an arbitrage-free model for the term structure of credit risk spreads and their evolution through time. This model will prove useful for the pricing and hedging of corporate debt with We would like to thank John Tierney of Lehman Brothers for providing the bond index price data, and Tal Schwartz for computational assistance. We would also like to acknowledge helpful comments received from an anonymous referee. Send all correspondence to Robert A. Jarrow, Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853. The Review of Financial Studies Summer 1997 Vol. 10, No. 2, pp. 481--523 1997 The Review of Financial Studies 0893-9454/97/$1.50 imbedded options, for the pricing and hedging of OTC derivatives with counterparty risk, for the pricing and hedging of (foreign) government bonds subject to default risk (e.g., municipal bonds), and for the pricing and hedging of credit derivatives (e.g. credit sensitive notes and spread adjusted notes). This model can also...

The views expressed are those of the authors and do not necessarily reflect those of the Bank of England. We thank Angus Guyatt for outstanding research support. We thank Reza Bahar, Patricia Jackson and other Bank of England colleagues for valuable comments and Angus Guyatt and Steve Grice for research assistance. Copies of working papers may be obtained from Publications Group, Bank of England,

In recent years, the number of downgrades in corporate bond ratings has exceeded the number of upgrades, leading some to conclude that the credit quality of U.S. corporate debt has declined. However, an alternative explanation of this apparent decline in credit quality is that the rating agencies are now using more stringent standards in assigning ratings. An ordered probit analysis of a panel of firms from 1978 through 1995 suggests that rating standards have indeed become more stringent, implying that at least part of the downward trend in ratings is the result of changing standards. BOND RATINGS PLAY A KEY ROLE in corporate financing and investment decisions. A corporation that can issue higher rated bonds usually receives better terms than one that can issue only lower rated bonds. By law or policy, some investors can purchase only bonds with an investment-grade rating, a restriction which in some asset pricing models would affect the relative prices of financial assets.

This article reports on an in-depth investigation of the expected ratings changes (drift) over time. Our analysis compares rating changes from the two major agencies, Moody's and S&P, over the period 1970-1996. For the first time, results from several studies which have documented and analyzed these data patterns are contrasted. Depending upon which study one uses, the results and implications can be very different. We expect that the findings will have implications for such diverse practitioners as bond investors who concentrate on any or all segments of the corporate bond market, eg., high yield bond and "crossover" investors, mark-to-market analysts, and traders in the new and growing market for credit-risk-derivatives and for the many analysts who properly view that credit quality assessment involves the entire spectrum of possible outcomes, not just default. A follow-up study will analyze, in greater depth, two critical characteristics of the rating drift phenomenon. These are unexpected, as well as expected, rating migration patterns and also the implied impact on the price of the fixed income instrument. 3 The Importance and Subtlety of Credit Rating Migration 1.0 Introduction and Purpose One of the most important indicators of a corporation's credit quality is the bond rating assigned to its outstanding, publicly traded indebtedness by independent rating agencies. After issuance and the assignment of the initial bond rating, these agencies perform reviews of the underlying issues, although it is not clear if these are periodic or based on market events -- probably both. If deemed warranted, these reviews result in a change, or drift, in the rating signifying improved (upgrade) or deteriorated (downgrade) in the issuers credit worthiness. Using both Moody's an...

Abstract Rating agencies are often subject to the criticism of being slow in adjusting their rating to current conditions. This paper examines the timeliness of rating changes and identifies factors which result in ’stickiness ’ of rating actions. Stickiness is characterized by not adjusting the rating even when a market-based estimate of default probability changes. Introducing an extended econometric model of friction the migration policy is modelled in terms of thresholds which have to be crossed by default probability estimates before an up- or downgrade occurs. Default probability estimates have to change by around two notches before the rating agency reacts. The timeliness differs across the rating spectrum and over the years. During periods with high defaults and for low credit quality firms agencies tend to rate more timely.

We explore sources of heterogeneity in rating migration behavior using a continuous time Markov chain. Working in continuous time circumvents of the embedding problem, allows for arbitrary prediction horizons, mitigates the censoring effect, and facilitates term structure modeling. By adopting a Bayesian estimation procedure we are able to estimate for each issuer profile its own continuous time Markov chain generator. Using the Moodys corporate bond default database we identify significant country and industry effects on the determi-nation of default intensity, rating migration volatility and conditional transition probabilities. We tabulate and compare these quantities for different issuer profiles to assess the heterogeneity in the sample. We compare the one year transition probability matrices for differ-ent profiles using Jaffry-Shuermann mobility metric. We show that other characteristics such as how long the issuer has been in existence, can also strongly affect the rating migration behavior. We therefore provide support and a tool for tailoring Markov chain generators to individual issuer profiles. The model may possibly be extended to in-corporate other time-varying covariates such as age and momentum; this is the focus of ongoing work. 2 1

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Motivation of the paper is to provide the investor community with insights to the nature of credit risk, empirical evidence, and existing models, while at the same time pointing out to the difficulties encountered when estimating credit risk due to specific features of the Swiss market (lack of ratings, illiquidity, taxation, etc.). The focus will be on the discussion of these special features since they have a strong impact on credit risk assessment. Privatization of the telecommunication and liberalization of the electricity sector, financial difficulties in the public sector in the 1990ies, the more short-lived high-tech sector exposed at the Swiss New Market, all examples that must lead the investor community to a greater degree of awareness of credit risk. The empirical section of the paper attempts to find potential