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42
BSLP: Markovian bivariate spreadloss model for portfolio credit derivatives
, 2007
"... BSLP is a twodimensional dynamic model of interacting portfoliolevel loss and loss intensity processes. It is constructed as a Markovian, shortrate intensity model, which facilitates fast lattice methods for pricing various portfolio credit derivatives such as tranche options, forwardstarting tr ..."
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Cited by 30 (0 self)
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BSLP is a twodimensional dynamic model of interacting portfoliolevel loss and loss intensity processes. It is constructed as a Markovian, shortrate intensity model, which facilitates fast lattice methods for pricing various portfolio credit derivatives such as tranche options, forwardstarting tranches, leveraged supersenior tranches etc. A semiparametric model specification is used to achieve near perfect calibration to any set of consistent portfolio tranche quotes. The onedimensional local intensity model obtained in the zero volatility limit of the stochastic intensity is useful in its own right for pricing nonstandard index tranches by arbitragefree interpolation. Opinions expressed in this paper are those of the authors, and do not necessarily reflect the view of
The Forward Loss Model: A Dynamic Term Structure Approach for the Pricing of Portfolio Credit Derivatives
, 2005
"... In this paper, we present the Forward Loss Model, a practical framework for the pricing of portfolio credit derivatives. The model is given in terms of a natural underlying, the forward loss, for which an HJMlike and a market model representation are provided. We give broad and flexible classes of ..."
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Cited by 26 (1 self)
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In this paper, we present the Forward Loss Model, a practical framework for the pricing of portfolio credit derivatives. The model is given in terms of a natural underlying, the forward loss, for which an HJMlike and a market model representation are provided. We give broad and flexible classes of underlying diffusions and assess the corresponding noarbitrage conditions. A simple, onefactor version of the FLM is implemented and calibrated to the iTraxx market. Implied term structure and dynamics of correlation are discussed, with the application to forward starting CDO, options on CDOs and Leverage Super Senior.
Calibration of CDO tranches with the dynamical generalizedPoisson loss model
 RISK
, 2006
"... In the first part we consider a dynamical model for the number of defaults of a pool of names. The model is based on the notion of generalized Poisson process, allowing for more than one default in small time intervals, contrary to many alternative approaches to loss modeling. We illustrate how to d ..."
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Cited by 25 (4 self)
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In the first part we consider a dynamical model for the number of defaults of a pool of names. The model is based on the notion of generalized Poisson process, allowing for more than one default in small time intervals, contrary to many alternative approaches to loss modeling. We illustrate how to define the pool default intensity and discuss recovery assumptions. The models are tractable, pricing and simulation are straightforward, and consistent calibration to quoted index CDO tranches and tranchelets for several maturities is feasible, as we illustrate with numerical examples. In the second part we model directly the pool loss and we introduce extensions based on piecewisegamma, scenariobased or CIR random intensities, leading to richer spread dynamics, investigating calibration improvements and stability.
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.
Dynamic models of portfolio credit risk: A simplified approach. Working paper
 Joshi, M S and A M Stacey
, 2006
"... We propose a simple dynamic model that is an attractive alternative to the (static) Gaussian copula model. The model assumes that the hazard rate of a company has a deterministic drift with periodic impulses. The impulse size plays a similar role to default correlation in the Gaussian copula model. ..."
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Cited by 16 (2 self)
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We propose a simple dynamic model that is an attractive alternative to the (static) Gaussian copula model. The model assumes that the hazard rate of a company has a deterministic drift with periodic impulses. The impulse size plays a similar role to default correlation in the Gaussian copula model. The model is analytically tractable and can be represented as a binomial tree. It can be calibrated so that it exactly matches the term structure of CDS spreads and provides a good fit to CDO quotes of all maturities. Empirical research shows that as the default environment worsens default correlation increases. Consistent with this research we find that in order to fit market data it is necessary to assume that as the default environment worsens impulse size increases. We present both a homogeneous and heterogeneous version of the model and provide results on the use of the calibrated model to value forward CDOs, CDO options, and leveraged super senior transactions. *We are grateful to Moody’s Investors Services for providing financial support for this research.
Portfolio Losses in Factor Models: Term Structure and Intertemporal Loss Dependence
 Journal of Credit Risk
"... Due to their computational efficiency, simple factor models remain popular in the pricing of credit portfolio derivatives. In this paper, we continue the elaboration on the fundamental structure of factor models initiated in [3], with a special focus on term structure effects. We describe a number o ..."
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Cited by 15 (0 self)
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Due to their computational efficiency, simple factor models remain popular in the pricing of credit portfolio derivatives. In this paper, we continue the elaboration on the fundamental structure of factor models initiated in [3], with a special focus on term structure effects. We describe a number of techniques to understand, and to improve control over, portfolio loss distribution term structures and intertemporal loss correlation. As part of our analysis, we introduce an extension of the RFL model ([2]) to incorporate jumps in the systematic factor and in firm residuals. We also numerically test the dependence of forwardstarting synthetic CDOs on the correlation of losses across time. Finally, our analysis highlights the fact that several of the models suggested in the literature are essentially equivalent. 1
Twodimensional Markovian model for dynamics of aggregate credit loss
 ADVANCES IN ECONOMETRICS
, 2007
"... We propose a new model for the dynamics of the aggregate credit portfolio loss. The model is Markovian in two dimensions with the state variables being the total accumulated loss Lt and the stochastic default intensity λt. The dynamics of the default intensity are governed by the equation dλt = κ(ρ( ..."
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Cited by 14 (1 self)
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We propose a new model for the dynamics of the aggregate credit portfolio loss. The model is Markovian in two dimensions with the state variables being the total accumulated loss Lt and the stochastic default intensity λt. The dynamics of the default intensity are governed by the equation dλt = κ(ρ(Lt, t) − λt)dt + σ √ λtdWt. The function ρ depends both on time t and accumulated loss Lt, providing sufficient freedom to calibrate the model to a generic distribution of loss. We develop a computationally efficient method for model calibration to the market of synthetic single tranche CDOs. The method is based on the Markovian projection technique which reduces the full model to a onestep Markov chain having the same marginal distributions of loss. We show that once the intensity function of the effective Markov chain consistent with the loss distribution implied by the tranches is found, the function ρ can be recovered with a very moderate computational effort. Because our model is Markovian and has low dimensionality, it offers a convenient framework for the pricing of dynamic credit instruments, such as options on indices and tranches, by backward induction. We calibrate the model to a set of recent market quotes on CDX index tranches and apply it to the pricing of tranche options.
Stochastic intensity modelling for structured credit exotics
 INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE
, 2006
"... We propose a class of credit models where we model default intensity as a jumpdiffusion stochastic process. We demonstrate how this class of models can be specialised to value multiasset derivatives such as CDO and CDO2 in an efficient way. We also suggest how it can be adapted to the pricing of o ..."
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Cited by 9 (0 self)
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We propose a class of credit models where we model default intensity as a jumpdiffusion stochastic process. We demonstrate how this class of models can be specialised to value multiasset derivatives such as CDO and CDO2 in an efficient way. We also suggest how it can be adapted to the pricing of option on tranche and leverage tranche deals. We discuss how the model performs when calibrated to the market.
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. ..."
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Cited by 8 (0 self)
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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.
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 ..."
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Cited by 6 (5 self)
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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