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

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

Motivated by recent financial crises in East Asia and the United States where the downfall of a small number of firms had an economy-wide impact, this paper generalizes existing reduced-form models to include default intensities dependent on the default of a counterparty. In this model, firms have correlated defaults due not only to an exposure to common risk factors, but also to firm-specific risks that are termed “counterparty risks.” Numerical examples illustrate the effect of counterparty risk on the pricing of defaultable bonds and credit derivatives such as default swaps.

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We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollar-denominated bonds. We consider the determinants of the Russian yield spread, the yield differential across different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios. THIS PAPER DEVELOPS A MODEL of the termstructure of credit spreads on sovereign bonds that accommodates: (i) Default or repudiation: The sovereign announces that it will stop making payments on its debt; (ii) Restructuring or renegotiation: The sovereign and the lenders ‘‘agree’ ’ to reduce (or postpone) the remaining payments; and (iii) A‘‘regime switch,’’such as a change of government or the default of another sovereign bond that changes the perceived risk of future defaults.We build on the framework of Duffie and Singleton (1999), showing that

We identify and estimate the sources of risk that cause corporate bonds to earn an excess return over default-free bonds. In particular, we estimate the risk premium associated with a default event. Default is modelled using a jump process with stochastic intensity. For a large set of firms, we model the default intensity of each firm as a function of common and firm-specific factors. In the model, corporate bond excess returns can be due to risk premia on factors driving the intensities and due to a risk premium on the default jump risk. The model is estimated using data on corporate bond prices for 104 US firms and historical default rate data. We find significant risk premia on the factors that drive intensities. However, these risk premia cannot fully explain the size of corporate bond excess returns. Next, we estimate the size of the default jump risk premium, correcting for possible tax and liquidity effects. The estimates show that this event risk premium is a significant and economically important determinant of excess corporate bond returns.

This is the first study that computes default measures for individual firms using Merton’s (1974) option pricing model, to assess the effect that default risk has on equity returns. We find that equally-weighted portfolios of stocks with high default probability earn significantly higher returns than equally-weighted portfolio of stocks with low default probability. In addition, both the size and book-to-market effects are present only within the portfolio of stocks with the highest default probabilities. Once stocks with the 30 % highest default probabilities are excluded from the sample, both size and B/M effects disappear. We also find that default risk is priced and can explain part of the cross-sectional variation in returns. The Fama-French factors SMB and HML, and particularly SMB, contain some default-related information, although it appears that this information is not the driving force behind the success of the Fama-French model. Keywords: default risk, equity returns, Merton’s (1974) model, size and book-to-market. JEL classification: G33, G12 1

wish to thank Andre Haris, Lozan Bakayatov, and Davron Yakubov for their excellent data collection efforts. In addition, we thank the financial assistance of the Social Sciences and Humanities Research Council of Canada. All errors remain the responsibility of the authors. Corporate Yield Spreads and Bond Liquidity We examine whether liquidity is priced in corporate yield spreads. Using a battery of liquidity measures covering over 4000 corporate bonds and spanning investment grade and speculative categories, we find that more illiquid bonds earn higher yield spreads; and that an improvement of liquidity causes a significant reduction in yield spreads. These results hold after controlling for common bond-specific, firm-specific, and macroeconomic variables, and are robust to issuers ’ fixed effect and potential endogeneity bias. Our finding mitigates the concern in the default risk literature that neither the level nor the dynamic of yield spreads can be fully explained by default risk determinants, and suggests that liquidity plays an important role in corporate bond valuation.

This paper is a critical survey of models designed for pricing fixed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specification of dynamic term structure models and their empirical fit to historical changes in the shapes of yield curves. We begin by overviewing the dynamic term structure models that have been fit to treasury or swap yield curves and in which the risk factors follow diffusions, jump-diffusion, or have “switching regimes. ” Then the goodness-of-fits of these models are assessed relative to their abilities to: (i) match linear projections of changes in yields onto the slope of the yield curve; (ii) match the persistence of conditional volatilities, and the shapes of term structures of unconditional volatilities, of yields; and (iii) to reliably price caps, swaptions, and other fixed-income derivatives. For the case of defaultable securities we explore the relative fits to historical yield spreads. 1

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.