Results 1  10
of
18
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 ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 16 (6 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
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.
Dynamic hedging of portfolio credit derivatives
, 2011
"... As shown by the recent turmoil in credit markets, much remains to be done for the proper risk management of credit derivatives. In particular, the static copulabased models commonly used for pricing portfolio credit derivatives appear to be inappropriate for hedging and risk management. We study he ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
As shown by the recent turmoil in credit markets, much remains to be done for the proper risk management of credit derivatives. In particular, the static copulabased models commonly used for pricing portfolio credit derivatives appear to be inappropriate for hedging and risk management. We study hedging of index CDO tranches with the underlying index default swap using various portfolio loss models which account for default contagion and spread risk. Numerical results obtained from models calibrated to iTraxx Europe data reveal significant differences in hedge ratios across models and show, unlike what had been previously suggested in the literature by comparing copulabased models, that hedging strategies are subject to substantial model risk. An empirical analysis based on recent market data shows that strategies based on deltahedging of spread movements have poorly performed during the 20072008 subprime crisis, while varianceminimizing hedges led to significantly smaller losses. Our empirical study also reveals that, while sudden large moves do occur in index spreads, these jumps do not necessarily occur on default dates of index constituents, an observation which contradicts the intuition conveyed by some recently proposed credit risk models.
unknown title
, 2011
"... We consider a bottomup Markovian model of portfolio credit risk where dependence among credit names stems from the possibility of simultaneous defaults. A common shocks interpretation of the model is possible so that efficient convolution recursion procedures are available for pricing and hedging C ..."
Abstract
 Add to MetaCart
We consider a bottomup Markovian model of portfolio credit risk where dependence among credit names stems from the possibility of simultaneous defaults. A common shocks interpretation of the model is possible so that efficient convolution recursion procedures are available for pricing and hedging CDO tranches, conditionally on any given state of the Markov model. Calibration of marginals and dependence parameters can be performed separately using a twosteps procedure, much like in a standard static copula setup. As a result this model allows us to hedge CDO tranches using singlename CDSs in a theoretically sound and practically convenient way. To illustrate this we calibrate the model against market data on CDO tranches and the underlying singlename CDSs. We then study the loss distributions as well as the minvariance hedging strategies in the calibrated portfolios.
PRICING BASKET DEFAULT SWAPS IN A TRACTABLE SHOTNOISE MODEL
"... Abstract. We value CDS spreads and kthtodefault swap spreads in a tractable shot noise model. The default dependence is modelled by letting the individual jumps of the default intensity be driven by a common latent factor. The arrival of the jumps is driven by a Poisson process. By using condition ..."
Abstract
 Add to MetaCart
Abstract. We value CDS spreads and kthtodefault swap spreads in a tractable shot noise model. The default dependence is modelled by letting the individual jumps of the default intensity be driven by a common latent factor. The arrival of the jumps is driven by a Poisson process. By using conditional independence and properties of the shot noise processes we derive tractable closedform expressions for the default distribution and the ordered survival distributions in a homogeneous portfolio. These quantities are then used to price and study CDS spreads and kthtodefault swap spreads as function of the model parameters. We study the kthtodefault spreads as function of the CDS spread, as well as other parameters in the model. All calibrations lead to perfect fits. Date: March 31, 2010. Key words and phrases. Credit risk, intensitybased models, dependence modelling, shot noise, CDS, kthtodefault swaps.