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61
Basket Default Swaps, CDO's and Factor Copulas
 JOURNAL OF RISK
, 2003
"... We consider a factor approach to the pricing of basket credit derivatives and synthetic CDO tranches. Our purpose is to deal in a convenient way with dependent defaults for a large number of names. We provide semiexplicit expressions of the stochastic intensities of default times and pricing formul ..."
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Cited by 79 (6 self)
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We consider a factor approach to the pricing of basket credit derivatives and synthetic CDO tranches. Our purpose is to deal in a convenient way with dependent defaults for a large number of names. We provide semiexplicit expressions of the stochastic intensities of default times and pricing formulae for basket default swaps and CDO tranches. Two cases are studied in detail: meanvariance mixture models and frailty models. We also compare prices under Gaussian and Clayton copulas.
Is credit event risk priced? Modeling contagion via the updating of beliefs
, 2003
"... We propose a reducedform model where jumpstodefault are priced because they generate a marketwide 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 ..."
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Cited by 48 (3 self)
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We propose a reducedform model where jumpstodefault are priced because they generate a marketwide 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 liquidityshock, 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 ‘flighttoquality ’ response in the Treasury market. A calibration argument suggests that the premium associated with jumptodefault risk for a typical investment grade firm has an upper bound of a few basis points per year, but that the risk premium for contagionrisk may be considerably larger.
Common failings: how corporate defaults are correlated
 Journal of Finance
, 2007
"... We test the doubly stochastic assumption under which firms ’ default times are correlated only as implied by the correlation of factors determining their default intensities. Using data on U.S. corporations from 1979 to 2004, this assumption is violated in the presence of contagion or “frailty ” (un ..."
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Cited by 44 (2 self)
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We test the doubly stochastic assumption under which firms ’ default times are correlated only as implied by the correlation of factors determining their default intensities. Using data on U.S. corporations from 1979 to 2004, this assumption is violated in the presence of contagion or “frailty ” (unobservable explanatory variables that are correlated across firms). Our tests do not depend on the timeseries properties of default intensities. The data do not support the joint hypothesis of wellspecified default intensities and the doubly stochastic assumption. We find some evidence of default clustering exceeding that implied by the doubly stochastic model with the given intensities. WHY DO CORPORATE DEFAULTS CLUSTER IN TIME? Several explanations have been explored. First, firms may be exposed to common or correlated risk factors whose comovements cause correlated changes in conditional default probabilities. Second, the event of default by one firm may be “contagious, ” in that one such event may directly induce other corporate failures, as with the collapse of Penn
Semiparametric Pricing of Multivariate Contingent Claims
, 1999
"... This paper derives and implements a nonparametric, arbitragefree technique for multivariate contingent claims (MVCC) pricing. This technique is based on nonparametric estimation of a multivariate riskneutral density function using data from traded options markets and historical asset returns. “New ..."
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Cited by 27 (2 self)
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This paper derives and implements a nonparametric, arbitragefree technique for multivariate contingent claims (MVCC) pricing. This technique is based on nonparametric estimation of a multivariate riskneutral density function using data from traded options markets and historical asset returns. “New ” multivariate claims are priced using expectations under this measure. An appealing feature of nonparametric arbitragefree derivative pricing is that fitted prices are obtained that are consistent with traded option prices and are not based on specific restrictions on the underlying asset price process or the functional form of the riskneutral density. Nonparametric MVCC pricing utilizes the method of copulas to combine nonparametrically estimated marginal riskneutral densities (based on options data) into a joint density using a separately estimated nonparametric dependence function (based on historical returns data). This paper provides theory linking objective and riskneutral dependence functions, and empirically testable conditions that justify the use of historical data for estimation of the riskneutral dependence function. The nonparametric MVCC pricing technique is implemented for the valuation of bivariate underperformance and outperformance options on the S&P500 and DAX index. Price deviations are
The Forward Loss Model: A Dynamic Term Structure Approach for the Pricing of Portfolio Credit Derivatives
, 2005
"... In this paper, we present the Forward Loss Model, a practical framework for the pricing of portfolio credit derivatives. The model is given in terms of a natural underlying, the forward loss, for which an HJMlike and a market model representation are provided. We give broad and flexible classes of ..."
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Cited by 26 (1 self)
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In this paper, we present the Forward Loss Model, a practical framework for the pricing of portfolio credit derivatives. The model is given in terms of a natural underlying, the forward loss, for which an HJMlike and a market model representation are provided. We give broad and flexible classes of underlying diffusions and assess the corresponding noarbitrage conditions. A simple, onefactor version of the FLM is implemented and calibrated to the iTraxx market. Implied term structure and dynamics of correlation are discussed, with the application to forward starting CDO, options on CDOs and Leverage Super Senior.
Portfolio credit risk models with interacting default intensities: a Markovian approach
, 2004
"... We consider reducedform models for portfolio credit risk with interacting default intensities. In this class of models the impact of default of some firm on the default intensities of surviving firms is exogenously specified and the dependence structure of the default times is endogenously determin ..."
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Cited by 17 (1 self)
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We consider reducedform models for portfolio credit risk with interacting default intensities. In this class of models the impact of default of some firm on the default intensities of surviving firms is exogenously specified and the dependence structure of the default times is endogenously determined. We construct and study the model using Markov process techniques. We analyze in detail a model where the interaction between firms is of the meanfield type. Moreover, we discuss the pricing of portfolio related credit products such as basket default swaps and CDOs in our model.
Pricing synthetic CDO tranches in a model with default contagion using the matrixanalytic approach
 CONTAGION IN PORTFOLIO CREDIT RISK 25
, 2007
"... We value synthetic CDO tranche spreads, index CDS spreads, k thtodefault swap spreads and tranchelets in an intensitybased credit risk model with default contagion. The default dependence is modelled by letting individual intensities jump when other defaults occur. The model is reinterpreted as ..."
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Cited by 17 (5 self)
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We value synthetic CDO tranche spreads, index CDS spreads, k thtodefault swap spreads and tranchelets in an intensitybased credit risk model with default contagion. The default dependence is modelled by letting individual intensities jump when other defaults occur. The model is reinterpreted as a Markov jump process. This allows us to use a matrixanalytic approach to derive computationally tractable closedform expressions for the credit derivatives that we want to study. Special attention is given to homogenous portfolios. For a fixed maturity of five years, such a portfolio is calibrated against CDO tranche spreads, index CDS spread and the average CDS spread, all taken from the iTraxx Europe series. After the calibration, which renders perfect fits, we compute spreads for tranchelets and k thtodefault swap spreads for different subportfolios of the main portfolio. Studies of the implied tranchelosses and the implied loss distribution in the calibrated portfolios are also performed. We implement two different numerical methods for determining the distribution of the Markovprocess. These are applied in separate calibrations in order to verify that the matrixanalytic method is independent of the numerical approach used to find the law of the process. Monte Carlo simulations are also performed to check the correctness of the numerical implementations.
A comparative analysis of CDO pricing models
 ISFA Actuarial School and BNP Parisbas
, 2005
"... We compare some popular CDO pricing models. Dependence between default times is modelled through Gaussian, stochastic correlation, Student t, double t, Clayton and MarshallOlkin copulas. We detail the model properties and compare the semianalytic pricing approach with large portfolio approximation ..."
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Cited by 14 (0 self)
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We compare some popular CDO pricing models. Dependence between default times is modelled through Gaussian, stochastic correlation, Student t, double t, Clayton and MarshallOlkin copulas. We detail the model properties and compare the semianalytic pricing approach with large portfolio approximation techniques. The ability of the models to fit the correlation skew observed in CDO market quotes is also assessed. Eventually, we relate CDO premiums and the distribution of conditional default probabilities which appears as a key input in the copula specification.