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Moody's Investors Service for financial support and for making their historical data on company ratings available to us. We are grateful to GFI for making their data on CDS spreads available to us. We are also grateful to Jeff Bohn, Richard Cantor, Yu Du, Darrell

This paper provides a methodology for valuing credit default swaps when the payoff is contingent on default by a single reference entity and there is no counterparty default risk. The paper tests the sensitivity of credit default swap valuations to assumptions about the expected recovery rate. It also tests whether approximate no-arbitrage arguments give accurate valuations and provides an example of the application of the methodology to real data. In a companion paper entitled Valuing Credit Default Swaps II: Modeling Default Correlation, the analysis is extended to cover situations where the payoff is contingent on default by multiple reference entities and situations where there is counterparty default risk.

This paper inv estigates the potential for extreme co-mov ements between financial assets by directly testing the underlying dependence structure. In particular, a t-dependence structure, deriv ed from the Student t distribution, is used as a proxy to test for this extremal behav#a(0 Tests in three di#erent markets (equities, currencies, and commodities) indicate that extreme co-mov ements are statistically significant. Moreov er, the "correlation-based" Gaussian dependence structure, underlying the multiv ariate Normal distribution, is rejected with negligible error probability when tested against the t-dependencealternativ e. The economic significance of these results is illustratedv ia three examples: co-mov ements across the G5 equity markets; portfoliov alue-at-risk calculations; and, pricing creditderiv ativ es. JEL Classification: C12, C15, C52, G11. Keywords: asset returns, extreme co-mov ements, copulas, dependence modeling, hypothesis testing, pseudo-likelihood, portfolio models, risk management. # The authorsw ould like to thankAndrew Ang, Mark Broadie, Loran Chollete, and Paul Glasserman for their helpful comments on an earlier version of this manuscript. Both authors arewS; the Columbia Graduate School of Business, e-mail: {rm586,assaf.zeevi}@columbia.edu, current version available at www.columbia.edu\# rm586 1 Introducti7 Specification and identification of dependencies between financial assets is a key ingredient in almost all financial applications: portfolio management, risk assessment, pricing, and hedging, to name but a few. The seminal work of Markowitz (1959) and the early introduction of the Gaussian modeling paradigm, in particular dynamic Brownian-based models, hav e both contributed greatly to making the concept of co rrelatio almost synony...

Due to their computational efficiency, simple factor models remain popular in the pricing of credit portfolio derivatives. In this paper, we continue the elaboration on the fundamental structure of factor models initiated in [3], with a special focus on term structure effects. We describe a number of techniques to understand, and to improve control over, portfolio loss distribution term structures and intertemporal loss correlation. As part of our analysis, we introduce an extension of the RFL model ([2]) to incorporate jumps in the systematic factor and in firm residuals. We also numerically test the dependence of forward-starting synthetic CDOs on the correlation of losses across time. Finally, our analysis highlights the fact that several of the models suggested in the literature are essentially equivalent. 1

group at Deutsche Bank in New York. The views in this paper are his own, and do not represent those of Deutsche Bank. Eric Neis is a Ph.D. student at the

In recent years, credit derivatives have become the main tool for transferring and hedging credit risk. The credit derivatives market has grown rapidly both in volume and in the breadth of the instruments it offers. Among the most complicated of these instruments are the multiname ones. These are instruments with payoffs that are contingent on the default realization in a portfolio of names. The modeling of dependent defaults is difficult because there is very little historical data available about joint defaults and because the prices of those instruments are not quoted. Therefore, the models cannot be calibrated, neither to defaults nor to prices. In this paper, we present a methodology for the estimation, simulation, and pricing of multiname contingent instruments. Our model is a hybrid of the well-known structural and reduced form approaches for modeling defaults. The dependence structure of our model is of a t-copula that possesses non-trivial tail dependence. The t-copula allows for more joint extreme events, which have a big impact on the prices of multiname instruments, e.g. n th-todefault baskets and CDOs. We demonstrate this impact with n th-to-default baskets. J.E.L. Subject Classification: G13.

The risk neutral credit migration process captures quantitative information which is relevant to the pricing theory and risk management of credit derivatives. In this article, we derive implied migration rates by means of a recently introduced credit barrier model which is calibrated on the basis of aggregate information such as credit migration rates and credit spread curves. The model is characterized by an underlying stochastic process that represents credit quality and default events are associated to barrier crossings. The stochastic process has state dependent volatility and jumps which are estimated by using empirical migration and default rates. A risk-neutralizing drift and forward liquidity spreads are estimated to consistently match the average spread curves corresponding to all the various ratings. The implied migration rates obtained with our credit barrier model are then compared with those obtained via the Jarrow-Lando-Turnbull model by the Kijima-Komoribayashi model in a detailed example.

ABSTRACT. The model introduced in this article is designed to provide a consistent representation for both the real-world and pricing measures for the credit process. We find that good agreement with historical and market data can be achieved across all credit ratings simultaneously. The model is characterized by an underlying stochastic process that represents credit quality and default events are associated to barrier crossings. The stochastic process has state dependent volatility and jumps which are estimated by using empirical migration and default rates. A risk-neutralizing drift and implied recovery rates are estimated to consistently match the average spread curves corresponding to all the various ratings. 1.

We consider intensity-based dynamic models for dependent defaults. We generalize the standard reduced-form models and assume that the default intensity of a firm is directly affected by the default of other firms in the portfolio. This interaction between defaults, which is termed counterparty risk in the literature, could be due to direct business relations between firms or due to the impact of defaults on the overall credit climate. We construct and study the model using Markov process techniques. We study in detail a model where the interaction between firms is of mean-field type.