This article presents convenient reduced-form models of the valuation of contingent claims subject to default risk, focusing on applications to the term structure of interest rates for corporate or sovereign bonds. Examples include the valuation of a credit-spread option

In the setting of ‘‘affine’ ’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks ’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.

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 purpose of this article is to explain the spread between spot rates on corporate and government bonds. We find that the spread can be explained in terms of three elements: (1) compensation for expected default of corporate bonds (2) compensation for state taxes since holders of corporate bonds pay state taxes while holders of government bonds do not, and (3) compensation for the additional systematic risk in corporate bond returns relative to government bond returns. The systematic nature of corporate bond return is shown by relating that part of the spread which is not due to expected default or taxes to a set of variables which have been shown to effect risk premiums in stock markets Empirical estimates of the size of each of these three components are provided in the paper. We stress the tax effects because it has been ignored in all previous studies of corporate bonds. 1

Abstract: We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm are a geometric Brownian motion until informed equityholders optimally liquidate, we derive the conditional distribution of the assets, given accounting data and survivorship. Contrary to the perfect-information case, there exists a default-arrival intensity process. That intensity is calculated in terms of the conditional distribution of assets. Credit yield spreads are characterized in terms of accounting information. Generalizations are provided. 1 We are exceptionally grateful to Michael Harrison for his significant contributions to this paper, which are noted within. We are also grateful for insightful research assistance

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.

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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.

We propose a reduced-form model where jumps-to-default are priced because they generate a market-wide jump in credit spreads. While this framework is consistent with a counterparty risk interpretation (e.g., Jarrow and Yu (2001)), it is most naturally interpreted as an updating of beliefs due to an unexpected event. Simple analytic solutions are obtained for the prices of risky debt regardless of the number of firms that share in the contagious response. As a special case, we show that the contagious response can be induced via a liquidity-shock, with no impact on actual default intensities. Empirically, we find that credit events of large firms generate a market wide increase in credit spreads and a significant ‘flight-to-quality ’ response in the Treasury market. A calibration argument suggests that the premium associated with jump-to-default risk for a typical investment grade firm has an upper bound of a few basis points per year, but that the risk premium for contagion-risk may be considerably larger.

1 Wewould like to thank Dan Chen, Louis Gagnon and participants in seminars at the Kansas City Federal Reserve and the Credit Risk Conference, Toronto, for their comments. We are especially grateful to two referees for their detailed suggestions on improving the paper's presentation and content. Although it will not evidence runtime errors, the program code presented in this paper is intended only as pseudo-code. Usage of the code is permitted with proper attribution, at the user's risk. This paper develops a framework for modelling risky debt and valuing credit derivatives that is exible and simple to implement, and that is, to the maximum extent possible, based on observables. Our approach is based on expanding the Heath-Jarrow-Morton term-structure model to allow for defaultable debt. We do not follow the procedure of implying out the behavior of spreads from assumptions concerning the default process, instead working directly with the evolution of spreads. We show that risk-neutral drifts in the resulting model possess a recursive representation that particularly facilitates implementation and makes it possible to handle path-dependence and early exercise features without di culty. The framework permits embedding a variety of speci cations for default; we present an empirical example of a default structure which provides promising calibration results. 1