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...

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Economic theory tells us that market and credit risks are intrinsically related to each other and not separable. We describe the two main approaches to pricing credit risky instruments: the structural approach and the reduced form approach. It is argued that the standard approaches to credit risk management -- CreditMetrics, CreditRisk+ and KMV -- are of limited value when applied to portfolios of interest rate sensitive instruments and in measuring market and credit risk. Empirically returns on high yield bonds have a higher correlation with equity index returns and a lower correlation with Treasury bond index returns than do low yield bonds. Also, macro economic variables appear to influence the aggregate rate of business failures. The CreditMetrics, CreditRisk+ and KMV methodologies cannot reproduce these empirical observations given their constant interest rate assumption. However, we can incorporate these empirical observations into the reduced form of Jarrow and Turnbull (1995b). Drawing the analogy. Risk 5, 63-70 model. Here default probabilities are correlated due to their dependence on common economic factors.

Warga, and the seminar participants at Indiana University and the Federal Reserve Bank of Kansas City. We also thank Klara Parrish for research assistance. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System. Credit Spreads and Interest Rates: A Cointegration Approach This paper uses cointegration to model the time-series of corporate and government bond rates. We show that corporate rates are cointegrated with government rates and the relation between credit spreads and Treasury rates depends on the time horizon. In the short-run, an increase in Treasury rates causes credit spreads to narrow. This effect is reversed over the long-run and higher rates cause spreads to widen. The positive long-run relation between spreads and Treasurys is inconsistent with prominent models for pricing corporate bonds, analyzing capital structure, and measuring the interest rate sensitivity of corporate bonds. 1.

ment at UCLA.

First passage models, where corporate assets undergo correlated random walks and a company defaults if its assets fall below a threshold provide an attractive framework for modeling the default process. Typical one year default correlations are small, i.e., of order a few percent, but nonetheless including correlations is very important, for managing portfolio credit risk and pricing some credit derivatives (e.g. first to default baskets). In first passage models the exact dependence of the joint survival probability of more than two firms on their asset correlations is not known. We derive an expression for the dependence of the joint survival probability of n firms on their asset correlations using first order perturbation theory in the correlations. It includes all terms that are linear in the correlations but neglects effects of quadratic and higher order. For constant time independent correlations we compare the first passage model expression for the joint survival probability with what a multivariate normal Copula function gives. As a practical application of our results we calculate the dependence of the five year joint survival probability for five basic industrials on their asset correlations. 1

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Any opinions expressed here are those of the author(s) and not those of the IIIS. All works posted here are owned and copyrighted by the author(s). Papers may only be downloaded for personal use only. Gady Jacoby† Department of Accounting and Finance, I.H. Asper School of Business,

www.elsevier.com/locate/econbase Default- and call-adjusted duration for corporate bonds