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,

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. This article presents a new approach to modeling term structures of bonds and other contingent claims that are subject to default risk. As in previous "reduced-form" models, we treat default as an unpredictable event governed by a hazard-rate process. 1 Our approach is distinguished by the parameterization of losses at default in terms of the fractional reduction in market value that occurs at default. Specifically, we fix some contingent claim that, in the event of no default, pays X at time T. We take as given an arbitrage-free setting in which all securities are priced in terms of some short-rate process r and equivalent martingale measure Q [see Harrison and Kreps (1979) and Harrison and Pliska (1981)]. Under this "risk-neutral" probability measure, we let h t denote the hazard rate for default at time t and let L t denote the expected fractional loss in market value if default were to occur at time t, conditional This article is a revised and extended version of the theoretical results from our earlier article "Econometric Modeling of Term Structures of Defaultable Bonds" (June 1994). The empirical results from that article, also revised and extended, are now found in "An Econometric Model of the Term Structure of Interest Rate Swap Yields" (Journal of Finance, October 1997). We are grateful for comments from many, including the anonymous referee, Ravi Jagannathan (the editor),

This paper explores the structural differences and relative goodness-of-fits of affine term structure models~ATSMs!. Within the family of ATSMs there is a tradeoff between f lexibility in modeling the conditional correlations and volatilities of the risk factors. This trade-off is formalized by our classification of N-factor affine family into N ϩ 1 non-nested subfamilies of models. Specializing to three-factor ATSMs, our analysis suggests, based on theoretical considerations and empirical evidence, that some subfamilies of ATSMs are better suited than others to explaining historical interest rate behavior.

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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.

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How does the market value "toxic" structured-credit securities? We study the valuation of what is possibly the most toxic of all toxic assets: the equity tranche of a CDO. In theory, CDO equity should be similar in nature to bank stock since both represent residual claims on a portfolio of loans. We find that CDO equity returns are much more related to stock returns than to fixed income returns. CDO equity returns track the returns of financial stocks much more closely than any other industry. Nearly two-thirds of the variation in CDO returns can be explained by fundamentals.

This paper explores the nature of default arrival and recovery implicit in the term structures of sovereign CDS spreads. We argue that term structures of spreads reveal not only the arrival rates of credit events (λ Q ), but also the loss rates given credit events. Applying our framework to Mexico, Turkey, and Korea, we show that a single-factor model with λ Q following a lognormal process captures most of the variation in the term structures of spreads. The risk premiums associated with unpredictable variation in λ Q are found to be economically significant and co-vary importantly with several economic measures of global event risk, financial market volatility, and macroeconomic policy.THE BURGEONING MARKET FOR SOVEREIGN CREDIT DEFAULT SWAPS (CDS) contracts offers a nearly unique window for viewing investors' risk-neutral probabilities of major credit events impinging on sovereign issuers, and their risk-neutral losses of principal in the event of a restructuring or repudiation of external debts. In contrast to many "emerging market" sovereign bonds, sovereign CDS contracts are designed without complex guarantees or embedded options. Trading activity in the CDS contracts of several sovereign issuers has developed to the point that they are more liquid than many of the underlying bonds. Moreover, in contrast to the corporate CDS market, where trading has been concentrated largely in the 5-year maturity contract, CDS contracts at several maturity points between 1 and 10 years have been actively traded for several years. As such, a full term structure of CDS spreads is available for inferring default and recovery information from market data. This paper explores in depth the time-series properties of the risk-neutral mean arrival rates of credit events (λ Q ) implicit in the term structure of sovereign CDS spreads. Applying our framework to Mexico, Turkey, and Korea, three countries with different geopolitical characteristics and credit ratings, we * Pan is with the MIT Sloan School of Management and NBER. Singleton is with the Graduate 2346The Journal of Finance find that single-factor models, in which country-specific λ Q follow lognormal processes, 1 capture most of the variation in the term structures of spreads. The maximum likelihood estimates suggest that, for all three countries, there are systematic, priced risks associated with unpredictable future variation in λ Q . Moreover, the time-series of the effects of risk premiums on CDS spreads covary strongly across countries. There are several large concurrent "run-ups" in risk premiums during our sample period (March 2001 through August 2006 that have natural interpretations in terms of political, macroeconomic, and financial market developments at the time.A more formal regression analysis of the correlations between risk premiums and the CBOE U.S. VIX option volatility index (viewed as a measure of event risk), the spread between the 10-year return on U.S. BB-rated industrial corporate bonds and the 6-month U.S. Treasury bill rate (viewed as a me...