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18
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
Understanding the Role of Recovery in Default Risk Models: Empirical Comparisons and Implied Recovery Rates
, 2006
"... This article presents a framework for studying the role of recovery on defaultable debt prices for a wide class of processes describing recovery rates and default probability. These debt models have the ability to differentiate the impact of recovery rates and default probability, and can be employe ..."
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Cited by 26 (0 self)
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This article presents a framework for studying the role of recovery on defaultable debt prices for a wide class of processes describing recovery rates and default probability. These debt models have the ability to differentiate the impact of recovery rates and default probability, and can be employed to infer the market expectation of recovery rates implicit in bond prices. Empirical implementation of these models suggests two central findings. First, the recovery concept that specifies recovery as a fraction of the discounted par value has broader empirical support. Second, parametric debt valuation models can provide a useful assessment of recovery rates embedded in bond prices.
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.
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
Modelling default contagion using Multivariate PhaseType distributions
, 2007
"... We model dynamic credit portfolio dependence by using default contagion in an intensitybased framework. Two different portfolios (with 10 obligors), one in the European auto sector, the other in the European financial sector, are calibrated against their market CDS spreads and the corresponding CD ..."
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Cited by 7 (3 self)
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We model dynamic credit portfolio dependence by using default contagion in an intensitybased framework. Two different portfolios (with 10 obligors), one in the European auto sector, the other in the European financial sector, are calibrated against their market CDS spreads and the corresponding CDScorrelations. After the calibration, which are perfect for the banking portfolio, and good for the auto case, we study several quantities of importance in active credit portfolio management. For example, implied multivariate default and survival distributions, multivariate conditional survival distributions, implied default correlations, expected default times and expected ordered defaults times. The default contagion is modelled by letting individual intensities jump when other defaults occur, but be constant between defaults. This model is translated into a Markov jump process, a so called multivariate phasetype distribution, which represents the default status in the credit portfolio. Matrixanalytic methods are then used to derive expressions for the quantities studied in the calibrated portfolios.
Pricing kthtodefault swaps under default contagion: the matrixanalytic approach
, 2006
"... We study a model for default contagion in intensitybased credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is transla ..."
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Cited by 6 (2 self)
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We study a model for default contagion in intensitybased credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is translated into a Markov jump process which represents the default status in the credit portfolio. This makes it possible to use matrixanalytic methods to derive computationally tractable closedform expressions for singlename credit default swap spreads and k thtodefault swap spreads. We ”semicalibrate” the model for portfolios (of up to 15 obligors) against market CDS spreads and compute the corresponding k thtodefault spreads. In a numerical study based on a synthetic portfolio of 15 telecom bonds we study a number of questions: how spreads depend on the amount of default interaction; how the values of the underlying market CDSprices used for calibration influence k ththto default spreads; how a portfolio with inhomogeneous recovery rates compares with a portfolio which satisfies the standard assumption of identical recovery rates; and, finally, how well k ththto default spreads in a nonsymmetric portfolio can be approximated by spreads in a symmetric portfolio.
Credit Risk in a Network Economy
, 2006
"... We develop a structural model of credit risk in a network economy, where any firm can lend to any other firm, so that each firm is subject to counterparty risk either from direct borrowers or from remote firms in the network. This model takes into account the role of each firm’s cash management. We ..."
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Cited by 4 (0 self)
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We develop a structural model of credit risk in a network economy, where any firm can lend to any other firm, so that each firm is subject to counterparty risk either from direct borrowers or from remote firms in the network. This model takes into account the role of each firm’s cash management. We show that we can obtain a semiclosed form formula for the price of debt and equity when cash accounts are buffers to bankruptcy risk. As in other structural models, the strategic bankruptcy decision of shareholders drives credit spreads, and differentiates debt from equity. Cash flow risk also causes credit risk interdependencies between firms. Our model applies to the case where not only financial flows but also operations are dependent across firms. We use queueing theory to obtain our semiclosed form formulae in steady state. We perform a simplified implementation of our model to the US automotive industry and show how we infer the impact on a supplier’s credit spreads of revenue changes in a manufacturer or even in a large car dealer. (Credit Risk; Contagion; Queueing Networks) 1
2013, ‘Default, liquidity and crises: an econometric framework
 Journal of Financial Econometrics
"... Preliminary version Abstract: In this paper, extending the work by Gourieroux, Monfort and Polimenis (2006) [78], we present a general discretetime affine framework aimed at jointly modeling yield curves that are associated with different issuers. The underlying fixedincome securities may differ i ..."
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Cited by 3 (2 self)
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Preliminary version Abstract: In this paper, extending the work by Gourieroux, Monfort and Polimenis (2006) [78], we present a general discretetime affine framework aimed at jointly modeling yield curves that are associated with different issuers. The underlying fixedincome securities may differ in terms of credit quality and/or in terms of liquidity. The risk factors follow discretetime Gaussian processes, with drifts and variancecovariance matrices that are subject to regime shifts described by a Markov chain with (historical) nonhomogenous transition probabilities. While flexible, the model remains tractable and amenable to empirical estimation. This is illustrated by an application on euroarea government yields. Specifically, the common dynamics of ten euroarea government yield curves are estimated using weekly data spanning the period from 1999 to early 2010. The dynamics of the yield curves are satisfyingly explained by both observable factors and unobservable ones. Among the latter, we exhibit a euroareawide liquidityrelated latent factor. The estimation results suggest that an important share of the changes in euroarea yield differentials is liquiditydriven.
A Liquidity Risk StressTesting Framework with Interaction between Market and Credit Risks,” Hong Kong Monetary Authority Working Paper 06/2009 (Hong Kong: Monetary Authority
, 2009
"... This study develops a stresstesting framework to assess liquidity risk of banks, where liquidity and default risks can stem from the crystallisation of market risk arising from a prolonged period of negative asset price shocks. In the framework, exogenous asset price shocks increase banks ’ liquidi ..."
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Cited by 3 (0 self)
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This study develops a stresstesting framework to assess liquidity risk of banks, where liquidity and default risks can stem from the crystallisation of market risk arising from a prolonged period of negative asset price shocks. In the framework, exogenous asset price shocks increase banks ’ liquidity risk through three channels. First, severe marktomarket losses on the banks ’ assets increase banks ’ default risk and thus induce significant deposits outflows. Secondly, the ability to generate liquidity from asset sales continues to evaporate due to the shocks. Thirdly, banks are exposed to contingent liquidity risk, as the likelihood of drawdowns on their irrevocable commitments increases in such stressful financial environments. In the framework, the linkage between market and default risks of banks is implemented using a Mertontype model, while the linkage between default risk and deposit outflows is estimated econometrically. Contagion risk is also incorporated through banks ’ linkage in the interbank and capital markets. Using the Monte Carlo method, the framework quantifies liquidity risk of individual banks by estimating the expected cashshortage time and the expected default time. Based on publicly available data as at the end of 2007, the framework is applied to a group of banks in Hong Kong. The simulation results suggest that liquidity risk of the banks would be contained in the face of a prolonged period of asset price shocks. However, some banks would be vulnerable when such shocks coincide with interest rate hikes due to monetary tightening. Such tightening is, however, relatively unlikely in a context of such shocks.