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15
Pricing and Hedging of Portfolio Credit Derivatives with Interacting Default Intensites
, 2007
"... We consider reducedform models for portfolio credit risk with interacting default intensities. In this class of models default intensities are modelled as functions of time and of the default state of the entire portfolio, so that phenomena such as default contagion or counterparty risk can be mode ..."
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Cited by 19 (1 self)
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We consider reducedform models for portfolio credit risk with interacting default intensities. In this class of models default intensities are modelled as functions of time and of the default state of the entire portfolio, so that phenomena such as default contagion or counterparty risk can be modelled explicitly. In the present paper this class of models is analyzed by Markov process techniques. We study in detail the pricing and the hedging of portfoliorelated credit derivatives such as basket default swaps and collaterized debt obligations (CDOs) and discuss the calibration to market data.
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.
Hedging Default Risks of CDOs in Markovian Contagion Models
 ISFA ACTUARIAL SCHOOL, UNIVERSITÉ DE LYON
, 2008
"... We describe a hedging strategy of CDO tranches based upon dynamic trading of the corresponding credit default swap index. We rely upon a homogeneous Markovian contagion framework, where only single defaults occur. In our framework, a CDO tranche can be perfectly replicated by dynamically trading the ..."
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Cited by 12 (2 self)
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We describe a hedging strategy of CDO tranches based upon dynamic trading of the corresponding credit default swap index. We rely upon a homogeneous Markovian contagion framework, where only single defaults occur. In our framework, a CDO tranche can be perfectly replicated by dynamically trading the credit default swap index and a riskfree asset. Default intensities of the names only depend upon the number of defaults and are calibrated onto an input loss surface. Numerical implementation can be carried out fairly easily thanks to a recombining tree describing the dynamics of the aggregate loss. Both continuous time market and its discrete approximation are complete. The computed credit deltas can be seen as a credit default hedge and may also be used as a benchmark to be compared with the market credit deltas. Though the model is quite simple, it provides some meaningful results which are discussed in detail. We study the robustness of the hedging strategies with respect to recovery rate and examine how input loss distributions drive the credit deltas. Using market inputs, we find that the deltas of the equity tranche are lower than those computed in the standard base correlation framework. This is related to the dynamics of dependence between defaults. We can think of our model as a “sticky implied tree” while the hedge ratios computed by market participants correspond to “sticky
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 6 (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.
Default contagion in large homogeneous portfolios
, 2008
"... We study default contagion in large homogeneous credit portfolios. Using data from the iTraxx Europe series, two synthetic CDO portfolios are calibrated against their tranche spreads, index CDS spreads and average CDS spreads, all with five year maturity. After the calibrations, which render perfe ..."
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Cited by 3 (2 self)
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We study default contagion in large homogeneous credit portfolios. Using data from the iTraxx Europe series, two synthetic CDO portfolios are calibrated against their tranche spreads, index CDS spreads and average CDS spreads, all with five year maturity. After the calibrations, which render perfect fits, we investigate the implied expected ordered defaults times, implied default correlations, and implied multivariate default and survival distributions, both for ordered and unordered default times. Many of the numerical results differ substantially from the corresponding quantities in a smaller inhomogeneous CDS portfolio. Furthermore, the studies indicate that market CDO spreads imply extreme default clustering in upper tranches. The default contagion is introduced by letting individual intensities jump when other defaults occur, but be constant between defaults. The model is translated into a Markov jump process. Expressions for the investigated quantities are derived by using matrixanalytic methods.
Pricing CDOs with State Dependent Stochastic Recovery Rates
, 2009
"... Up to the 2007 crisis, research within bottom‐up CDO models mainly concentrated on the dependence between defaults. However, due to the substantial increase in the market price of systemic credit risk protection, more attention has been paid to recovery rate assumptions. In this paper, we focus firs ..."
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Cited by 3 (0 self)
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Up to the 2007 crisis, research within bottom‐up CDO models mainly concentrated on the dependence between defaults. However, due to the substantial increase in the market price of systemic credit risk protection, more attention has been paid to recovery rate assumptions. In this paper, we focus first on deterministic recovery rates in a factor copula framework. We use stochastic orders theory to assess the impact of a recovery markdown on CDOs and show that it leads to an increase of the expected loss on senior tranches, even though the expected loss on the portfolio is kept fixed. This result applies to a wide range of latent factor models. We then suggest introducing stochastic recovery rates in such a way that the conditional on the factor expected loss (or equivalently the large portfolio approximation) is the same as in the recovery markdown case. However, granular portfolios behave differently. We show that a markdown is associated with riskier portfolios that when using the stochastic recovery rate framework. As a consequence, the expected loss on a senior tranche is larger in the former case, whatever the attachment point. We also deal with implementation and numerical issues related to the pricing of CDOs within the
An extension of Davis and Lo’s contagion model ∗
, 2010
"... Abstract: The present paper provides a multiperiod contagion model in the credit risk field. Our model is an extension of Davis and Lo’s infectious default model. We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also po ..."
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Abstract: The present paper provides a multiperiod contagion model in the credit risk field. Our model is an extension of Davis and Lo’s infectious default model. We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also possible). The spontaneous default without external influence and the infections are described by not necessarily independent Bernoullitype random variables. Moreover, several contaminations could be required to infect another firm. In this paper we compute the probability distribution function of the total number of defaults in a dependency context. We also give a simple recursive algorithm to compute this distribution in an exchangeability context. Numerical applications illustrate the impact of exchangeability among direct defaults and among contaminations, on different indicators calculated from the law of the total number of defaults. We then examine the calibration of the model on iTraxx data before and during the crisis. The dynamic feature together with the contagion effect seem to have a significant impact on the model performance, especially during the recent distressed period.
Deltahedging Correlation Risk?
, 2010
"... The Gaussian copula model is essentially a static quotation device, and its use for hedging is, in principle, questionable. The Gaussian copula delta thus assumes a constant tranche correlation, whereas in practice this correlation is dynamic, and correlated in particular to the credit index. It mig ..."
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The Gaussian copula model is essentially a static quotation device, and its use for hedging is, in principle, questionable. The Gaussian copula delta thus assumes a constant tranche correlation, whereas in practice this correlation is dynamic, and correlated in particular to the credit index. It might therefore be expected that a dynamic model of credit risk, able to capture at least part of the dependence between implied correlation and index spreads, should have better hedging performances. In this paper, we compare two deltas which can be used for hedging a CDO tranche by its credit index: the market or Gaussian copula delta, and the local intensity delta, where the latter refers to the delta in a local intensity default model of portfolio credit risk, recalibrated to the market every day. A theoretical analysis is illustrated by data analysis and backtesting hedging experiments based on both precrisis and crisis market data. We observe that hedging performance are comparable for crisis period associated with CDX Series 9 and 10. However, the local intensity delta fails to outperform the market delta in precrisis period associated with CDX Series 5, even if the local intensity model is a sound, dynamic model of credit risk, fitting the market over the full set of CDO tranches, as opposed to a static model and a per tranche fit in the case of the Gaussian copula model.
A MultiPortfolio Model for Bespoke CDO Pricing Part I: Methodology
, 2009
"... This paper presents a dynamic multiportfolio default model for consistent and arbitragefree pricing synthetic CDO tranches that reference a bespoke portfolio. In order to incorporate standard tranche price information, we assume that the bespoke portfolio has name overlapping with some index portfo ..."
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This paper presents a dynamic multiportfolio default model for consistent and arbitragefree pricing synthetic CDO tranches that reference a bespoke portfolio. In order to incorporate standard tranche price information, we assume that the bespoke portfolio has name overlapping with some index portfolios. Dividing the total portfolio (parent) into nonoverlapping subportfolios (children), and assuming homogeneity for both the parent and the children, we use a topdown dynamic default intensity model for the parent, and specify the conditional probability of default in the children given imminent default in the parent. We consider two fundamental cases which are building blocks of more complex applications: (a) the parent is an index and the bespoke is a child; and (b) the bespoke is the parent that contains one or more indices as children. When the parent is the index, the parent default process is uniquely determined independent of the children, and the child conditional default probability distribution is calibrated to the spreads of the children. When the bespoke is the parent and one or more children are indexes, we simultaneously calibrate the parent default intensity model and the child default probability to the standard tranches and child portfolio spreads. The model is designed to establish consistency between the pricing of standard tranches and the pricing of bespoke tranches. Application may include Portfolio enlargement where the bespoke tranche references a “global ” portfolio that contains “regional ” indexes as subportfolio. For example, tranches referencing CDX.NA.IG and iTraxx Europe. Portfolio thinning where the bespoke tranche references a subportfolio of an index. Combination of portfolio enlargement and thinning. For example, tranche referencing a subset of CDX and a subset of iTraxx. * Risk Management, The Depository Trust & Clearing Corporation.