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48
Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market
 Journal of Finance
, 2005
"... Copyright c○2004 by the authors. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. ..."
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Cited by 185 (4 self)
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Copyright c○2004 by the authors. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.
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 48 (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
Frailty Correlated Default
, 2008
"... This paper shows that the probability of extreme default losses on portfolios of U.S. corporate debt is much greater than would be estimated under the standard assumption that default correlation arises only from exposure to observable risk factors. At the high confidence levels at which bank loan p ..."
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Cited by 34 (2 self)
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This paper shows that the probability of extreme default losses on portfolios of U.S. corporate debt is much greater than would be estimated under the standard assumption that default correlation arises only from exposure to observable risk factors. At the high confidence levels at which bank loan portfolio and CDO default losses are typically measured for economiccapital and rating purposes, our empirical results indicate that conventionally based estimates are downward biased by a full order of magnitude on test portfolios. Our estimates are based on U.S. public nonfinancial firms existing between 1979 and 2004. We find strong evidence for the presence of common latent factors, even when controlling for observable factors that provide the most accurate available model of firmbyfirm default probabilities. ∗ We are grateful for financial support from Moody’s Corporation and Morgan Stanley, and for research assistance from Sabri Oncu and Vineet Bhagwat. We are also grateful for remarks from Torben Andersen, André Lucas, Richard Cantor, Stav Gaon, Tyler Shumway, and especially Michael Johannes. This revision is much improved because of suggestions by a referee, an associate editor, and Campbell Harvey. We are thankful to Moodys and to Ed Altman for generous assistance with data. Duffie is at The Graduate School of Business, Stanford University. Eckner and Horel are at Merrill Lynch. Saita is at Lehman
A general formula for valuing defaultable securities
 Econometrica
, 2004
"... Previous research has shown that under a suitable nojump condition, the price of a defaultable security is equal to its riskneutral expected discounted cash flows if a modified discount rate is introduced to account for the possibility of default. Below, we generalize this result by demonstrating ..."
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Cited by 17 (0 self)
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Previous research has shown that under a suitable nojump condition, the price of a defaultable security is equal to its riskneutral expected discounted cash flows if a modified discount rate is introduced to account for the possibility of default. Below, we generalize this result by demonstrating that one can always value defaultable claims using expected riskadjusted discounting provided that the expectation is taken under a slightly modified probability measure. This new probability measure puts zero probability on paths where default occurs prior to the maturity, and is thus only absolutely continuous with respect to the riskneutral probability measure. After establishing the general result and discussing its relation with the existing literature, we investigate several examples for which the nojump condition fails. Each example illustrates the power of our general formula by providing simple analytic solutions for the prices of defaultable securities.
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.
Dynamic hedging of synthetic CDO tranches with spread risk and default contagion
, 2007
"... We study the hedging of synthetic CDO tranches in a dynamic portfolio credit risk model which incorporates spread risk and default contagion. The model is constructed and studied via Markovchain techniques. We discuss the immunization of a CDO tranche against spread and event risk in the Markovch ..."
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Cited by 16 (6 self)
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We study the hedging of synthetic CDO tranches in a dynamic portfolio credit risk model which incorporates spread risk and default contagion. The model is constructed and studied via Markovchain techniques. We discuss the immunization of a CDO tranche against spread and event risk in the Markovchain model and compare the results with hedge ratios obtained in the standard Gauss copula model. Moreover, we derive modelbased dynamic hedging strategies using the concept of risk minimization. Numerical experiments are used to illustrate some of the properties of the riskminimizing hedging strategies.
Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk
, 2005
"... We propose a twosided jump model for credit risk by extending the LelandToft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of e ..."
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Cited by 13 (0 self)
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We propose a twosided jump model for credit risk by extending the LelandToft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of equity options: (1) The jump and endogenous default can produce a variety of nonzero credit spreads, including upward, humped, and downward shapes; interesting enough, the model can even produce, consistent with empirical findings, upward credit spreads for speculative grade bonds. (2) The jump risk leads to much lower optimal debt/equity ratio; in fact, with jump risk, highly risky firms tend to have very little debt. (3) The twosided jumps lead to a variety of shapes for the implied volatility of equity options, even for long maturity options; and although in generel credit spreads and implied volatility tend to move in the same direction under exogenous default models, but this may not be true in presence of endogenous default and jumps. In terms of mathematical contribution, we give a proof of a version of the “smooth fitting ” principle for the jump model, justifying a conjecture first suggested by Leland and Toft under the Brownian model. 1
When Do Firms Default? A Study of the Default Boundary
, 2007
"... This paper studies whether default is triggered by low market asset values or by liquidity shortages, corresponding to economic versus financial distress. Default is often assumed to occur when market assets fall below a certain boundary. Consistent with this hypothesis, some lowvalue firms default ..."
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Cited by 11 (2 self)
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This paper studies whether default is triggered by low market asset values or by liquidity shortages, corresponding to economic versus financial distress. Default is often assumed to occur when market assets fall below a certain boundary. Consistent with this hypothesis, some lowvalue firms default despite sufficient liquidity. However, liquidity shortages can precipitate default at high asset values when firms are restricted from accessing external financing. Moreover, many distressed firms do not default for years. As a result, even though boundarybased default predictions can match observed average default frequencies, they misclassify a large number of firms in crosssection.
Modeling the recovery rate in a reduced form model. Unpublished working paper
, 2005
"... This paper provides a model for the recovery rate process in a reduced form model. After default, a firm continues to operate, and the recovery rate is determined by the value of the firm’s assets relative to its liabilities. The debt recovers a different magnitude depending upon whether or not the ..."
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Cited by 9 (1 self)
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This paper provides a model for the recovery rate process in a reduced form model. After default, a firm continues to operate, and the recovery rate is determined by the value of the firm’s assets relative to its liabilities. The debt recovers a different magnitude depending upon whether or not the firm enters insolvency and bankruptcy. Although this recovery rate process is similar to that used in a structural model, the reduced form approach is maintained by utilizing information reduction in the sense of Guo, Jarrow and Zeng (2005). Our model is able to provide analytic expressions for a firm’s default intensity, bankruptcy intensity, and zerocoupon bond prices both before and after default. KEY WORDS: credit risk, recovery rates, reduced form model, filtration reduction ∗ Helpful comments from seminar participants at Cornell University, the Johannes
2009, Pricing Credit Derivatives under Incomplete Information: a NonlinearFiltering Approach
"... Abstract This paper considers a general reduced form pricing model for credit derivatives where default intensities are driven by some factor process X. The process X is not directly observable for investors in secondary markets; rather, their information set consists of the default history and of n ..."
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Cited by 8 (5 self)
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Abstract This paper considers a general reduced form pricing model for credit derivatives where default intensities are driven by some factor process X. The process X is not directly observable for investors in secondary markets; rather, their information set consists of the default history and of noisy price observation for traded credit products. In this context the pricing of credit derivatives leads to a challenging nonlinear filtering problem. We provide recursive updating rules for the filter, derive a finite dimensional filter for the case where X follows a finite state Markov chain and propose a novel particle filtering algorithm. A numerical case study illustrates the properties of the proposed algorithms.