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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.

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

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This paper provides an alternative approach to Duffe and Lando [7] for obtaining a reduced form credit risk model from a structural model.

of Greg Du�ee and Tyler Shumway have improved this paper. The views expressed herein are the authors own and

Credit Management for help with the data. We are also grateful for helpful comments to participants at a University of Verona conference and a seminar at the Q-Group. We are responsible for all remaining errors.

helpful comments on earlier drafts of this paper. Needless to say we are fully responsible for the content of the paper. 1 Merton’s Model, Credit Risk, and Volatility Skews In 1974 Robert Merton proposed a model for assessing the credit risk of a company by characterizing the company’s equity as a call option on its assets. In this paper we propose a way the model’s parameters can be estimated from the implied volatilities of options on the company’s equity. We use data from the credit default swap market to compare our implementation of Merton’s model with the traditional implementation approach. 2

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Prices of equity index put options contain information on the price of systematic downward jump risk. We use a structural jump-diffusion firm value model to assess the level of credit spreads that is generated by option-implied jump risk premia. In our compound option pricing model, an equity index option is an option on a portfolio of call options on the underlying firm values. We calibrate the model parameters to historical information on default risk, the equity premium and equity return distribution, and S&P 500 index option prices. Our results show that a model without jumps fails to fit the equity return distribution and option prices, and generates a low out-of-sample prediction for credit spreads. Adding jumps and jump risk premia improves the fitofthe model in terms of equity and option characteristics considerably and brings predicted credit spread levels much closer to observed levels.