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...

Using dealer’s quotes and transactions prices on straight industrial bonds, we investigate the determinants of credit spread changes. Variables that should in theory determine credit spread changes have rather limited explanatory power. Further, the residuals from this regression are highly cross-correlated, and principal components analysis implies they are mostly driven by a single common factor. Although we consider several macroeconomic and financial variables as candidate proxies, we cannot explain this common systematic component. Our results suggest that monthly credit spread changes are principally driven by local supply0 demand shocks that are independent of both credit-risk factors and standard proxies for liquidity.

the problems and opportunities facing the financial services industry in its search for competitive excellence. The Center's research focuses on the issues related to managing risk at the firm level as well as ways to improve productivity and performance. The Center fosters the development of a community of faculty, visiting scholars and Ph.D. candidates whose research interests complement and support the mission of the Center. The Center works closely with industry executives and practitioners to ensure that its research is informed by the operating realities and competitive demands facing industry participants as they pursue competitive excellence. Copies of the working papers summarized here are available from the Center. If you would like to learn more about the Center or become a member of our research community, please let us know of your interest.

This paper empirically tests five structural models of corporate bond pricing: those of Merton (1974), Geske (1977), Leland and Toft (1996), Longsta# and Schwartz (1995), and Collin-Dufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capital structures during the period 1986-1997. The conventional wisdom is that structural models do not generate spreads as high as those seen in the bond market, and true to expectations we find that the predicted spreads in our implementation of the Merton model are too low. However, most of the other structural models predict spreads that are too high on average. Nevertheless, accuracy is a problem, as the newer models tend to severely overstate the credit risk of firms with high leverage or volatility and yet su#er from a spread underprediction problem with safer bonds. The Leland and Toft model is an exception in that it overpredicts spreads on most bonds, particularly those with high coupons. More accurate structural models must avoid features that increase the credit risk on the riskier bonds while scarcely a#ecting the spreads of the safest bonds.

This paper analyzes the association between aggregate default and recovery rates on credit assets, and seeks to empirically explain this critical relationship. We examine recovery rates on corporate bond defaults, over the period 1982-2002. Our econometric univariate and multivariate models explain a significant portion of the variance in bond recovery rates aggregated across all seniority and collateral levels. The central thesis is that aggregate recovery rates are basically a function of supply and demand for the securities, with default rates playing a pivotal role. Such a link would bring about a significant increase in both expected and unexpected losses as measured by some widespread credit risk models, and would affect the procyclicality effects of the New Basel Capital Accord. Our results have also important implications for investors in corporate bonds and bank loans, and for all markets (e.g., securitizations, credit derivatives, etc.) which depend on recovery rates as a key variable.

Abstract not found

The recent accounting scandals at Enron, WorldCom, and Tyco were related to the misrepresentation of liabilities. We provide a structural model of correlated multi-firm default, in which public bond investors are uncertain about the liability-dependent barrier at which individual firms default. In lack of complete information, investors form prior beliefs on the barriers, which they update with the default status information of firms arriving over time. Whenever a firm suddenly defaults, investors learn about the default threshold of closely associated business partner firms. Due to the unpredictable nature of defaults in our model, this updating leads to "contagious" jumps in credit spreads of business partner firms, which correspond to re-assessments of these firms' health by investors. We characterize joint default probabilities and the default dependence structure as assessed by imperfectly informed investors, where we emphasize the the modeling of dependence with copulas.

Default probabilities are important to the credit markets. Changes in default probabilities may forecast credit rating migrations to other rating levels or to default. Such rating changes can affect the firm’s cost of capital, credit spreads, bond returns, and the prices and hedge ratios of credit derivatives. While rating agencies such as Moodys and Standard & Poors compute historical default frequencies, option models can also be used to calculate forward looking or expected default frequencies. In this paper, we compute risk neutral probabilities or default (RNPD) using the diffusion models of Merton (1974) and Geske (1977). It is shown that the Geske model produces a term structure of RNPD’s, and the shape of this term structure may forecast impending credit events. Next, it is shown that these RNPD’s serve as bounds to estimates of actual default probabilities. Furthermore, the RNPD’s exhibit the same comparative statics as the estimates of actual default probabilities. Also, the risk neutral default probabilities may be more accurately estimated than actual default probabilities because they do not require an estimate of the firm’s drift. Given these similarities and advantages of RNPD’s, their estimates may possess significant information about credit events. To confirm this an event study of the relation between RNPD

We test the theoretical equivalence of credit default swap (CDS) prices and credit spreads derived by Duffie (1999), finding support for the parity relation as an equilibrium condition. We also find two forms of deviation from parity. First, for three firms, CDS prices are substantially higher than credit spreads for long periods of time, arising from combinations of imperfections in the contract specification of CDSs and measurement errors in computing the credit spread. Second, we find short-lived deviations from parity for all other companies due to a lead for CDS prices over credit spreads in the price discovery process.

This paper presents a semi-analytical valuation method for basket credit derivatives in a flexible intensity-based model. Default intensities are mod-eled as correlated affine jump-diffusions. An empirical application docu-ments that the model fits market prices of benchmark basket credit deriva-tives reasonably well, consistent with the observed correlation skew. Hence, I argue, contrary to comments in the literature, that intensity-based port-folio credit risk models can be both tractable and capable of generating realistic levels of default correlation.