Results 1  10
of
23
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 31 (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.
A dynamic approach to the modelling of correlation credit derivatives using Markov chains
, 2006
"... The modelling of credit events is in effect the modelling of the times to default of various names. The distribution of individual times to default can be calibrated from CDS quotes, but for more complicated instruments, such as CDOs, the joint law is needed. Industry practice is to model this corre ..."
Abstract

Cited by 30 (0 self)
 Add to MetaCart
The modelling of credit events is in effect the modelling of the times to default of various names. The distribution of individual times to default can be calibrated from CDS quotes, but for more complicated instruments, such as CDOs, the joint law is needed. Industry practice is to model this correlation using a copula or base correlation approach, both of which suffer significant deficiencies. We present a new approach to default correlation modelling, where defaults of different names are driven by a common continuoustime Markov process. Individual default probabilities and default correlations can be calculated in closed form. As illustrations, CDO tranches with namedependent random losses are computed using Laplace transform techniques. The model is calibrated to standard tranche spreads with encouraging results.
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 ..."
Abstract

Cited by 29 (5 self)
 Add to MetaCart
(Show Context)
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.
Multiscale intensity models and name grouping for valuation of multiname credit derivatives
 Appl. Math. Finance
"... Abstract. The pricing of collateralized debt obligations and other basket credit derivatives is contingent upon (i) a realistic modeling of the firms ’ default times and the correlation between them, and (ii) efficient computational methods for computing the portfolio loss distribution from the indi ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
Abstract. The pricing of collateralized debt obligations and other basket credit derivatives is contingent upon (i) a realistic modeling of the firms ’ default times and the correlation between them, and (ii) efficient computational methods for computing the portfolio loss distribution from the individual firms ’ default time distributions. Factor models, a widelyused class of pricing models, are computationally tractable despite the large dimension of the pricing problem, thus satisfying issue (ii), but to have any hope of calibrating CDO data, numerically intense versions of these models are required. We revisit the intensitybased modeling setup for basket credit derivatives and, with the aforementioned issues in mind, we propose improvements (a) via incorporating fast meanreverting stochastic volatility in the default intensity processes, and (b) by considering homogeneous groups within the original set of firms. This can be thought of as a hybrid of topdown and bottomup approaches. We present a calibration example, including data in the midst of the 2008 financial credit crisis, and discuss the relative performance of the framework. 1.
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 14 (3 self)
 Add to MetaCart
(Show Context)
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.
Background Filtrations and Canonical Loss Processes for TopDown Models of Portfolio Credit Risk
, 2006
"... In singleobligor default risk modelling, using a background filtration in conjunction with a suitable embedding hypothesis (generally known as Hhypothesis or immersion property) has proven a very successful tool to separate the actual default event from the model for the default arrival intensity. ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
In singleobligor default risk modelling, using a background filtration in conjunction with a suitable embedding hypothesis (generally known as Hhypothesis or immersion property) has proven a very successful tool to separate the actual default event from the model for the default arrival intensity. In this paper we analyze the conditions under which this approach can be extended to the situation of a portfolio of several obligors, with a particular focus on the socalled topdown approach. We introduce the natural Hhypothesis of this setup (the successive Hhypothesis) and show that it is equivalent to a seemingly weaker onestep Hhypothesis. Furthermore, we provide a canonical construction of a loss process in this setup and provide closedform solutions for some generic pricing problems.
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 12 (3 self)
 Add to MetaCart
(Show Context)
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.
UP AND DOWN CREDIT RISK
, 2008
"... This paper discusses the main modeling approaches that have been developed so far for handling portfolio credit derivatives. In particular the so called top, top down and bottom up approaches are considered. We first provide an overview of these approaches. Then we give some mathematical insights to ..."
Abstract

Cited by 10 (7 self)
 Add to MetaCart
(Show Context)
This paper discusses the main modeling approaches that have been developed so far for handling portfolio credit derivatives. In particular the so called top, top down and bottom up approaches are considered. We first provide an overview of these approaches. Then we give some mathematical insights to the fact that information, namely, the choice of a relevant model filtration, is the major modeling issue. In this regard, we examine the notion of thinning that was recently advocated for the purpose of hedging a multiname derivative by singlename derivatives. We then give a further analysis of the various approaches using simple models, discussing in each case the issue of possibility of hedging. Finally we explain by means of numerical simulations (semistatic hedging experiments) why and when the portfolio loss process may not
Pricing Interest RateSensitive Credit Portfolio Derivatives
, 2006
"... In this paper we present a modelling framework for portfolio credit risk which incorporates the dependence between riskfree interestrates and the default loss process. The contribution in this approach is that – besides the traditional diffusionbased covariation between loss intensities and inter ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
In this paper we present a modelling framework for portfolio credit risk which incorporates the dependence between riskfree interestrates and the default loss process. The contribution in this approach is that – besides the traditional diffusionbased covariation between loss intensities and interestrates – a direct dependence between interestrates and the loss process is allowed, in particular defaultfree interestrates can also depend on the loss history of the credit portfolio. Amongst other things this enables us to capture the effect that economywide default events are likely to have on government bond markets and/or central banks ’ interestrate policies. Similar to Schönbucher (2005), the model is set up using a set of losscontingent forward interestrates fn(t, T) and losscontingent forward credit protection rates Fn(t, T) to parameterize the market prices of defaultfree bonds and creditsensitive assets such as CDOs. We show that (up to weak regularity conditions), existence of such a parametrization is necessary and sufficient for the absence of static arbitrage opportunities in the underlying assets. We also give necessary conditions and sufficient conditions on the dynamics of the parametrization which ensure absence of dynamic arbitrage opportunities in the model. Similar to the HJM drift restrictions for defaultfree interestrates, these conditions take the form of restrictions on the drifts of fn(t, T) and Fn(t, T), together with a set of regularity conditions.