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Bounded solutions to Backward SDE’s with jumps for utility optimization and indifference
"... We prove results on bounded solutions to backward stochastic equations driven by random measures. Those bounded BSDE solutions are then applied to solve different stochastic optimization problems with exponential utility in models where the underlying filtration is noncontinuous. This includes resul ..."
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Cited by 45 (0 self)
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We prove results on bounded solutions to backward stochastic equations driven by random measures. Those bounded BSDE solutions are then applied to solve different stochastic optimization problems with exponential utility in models where the underlying filtration is noncontinuous. This includes results on portfolio optimization under an additional liability and on dynamic utility indifference valuation and partial hedging in incomplete financial markets which are exposed to risk from unpredictable events. In particular, we characterize the limiting behavior of the utility indifference hedging strategy and of the indifference value process for vanishing risk aversion. 1. Introduction. A
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 31 (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 24 (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.
PRICING AND TRADING CREDIT DEFAULT SWAPS IN A HAZARD PROCESS MODEL
, 2005
"... An inspection of the existing literature in the area of credit risk shows that the vast majority of papers focus on the riskneutral valuation of credit derivatives without even mentioning the issue of hedging. This is somewhat surprising since, as is well known, the major argument supporting the ri ..."
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Cited by 17 (9 self)
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An inspection of the existing literature in the area of credit risk shows that the vast majority of papers focus on the riskneutral valuation of credit derivatives without even mentioning the issue of hedging. This is somewhat surprising since, as is well known, the major argument supporting the riskneutral valuation is the existence of hedging strategies for attainable contingent claims. In this
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 10 (7 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
Completeness of a general semimartingale markets under constrained trading. Working paper
, 2004
"... In this note, we provide a rather detailed and comprehensive study of the basic properties of selffinancing trading strategies in a general security market model driven by discontinuous semimartingales. Our main goal is to analyze the issue of replication of a generic contingent claim using a self ..."
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Cited by 10 (8 self)
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In this note, we provide a rather detailed and comprehensive study of the basic properties of selffinancing trading strategies in a general security market model driven by discontinuous semimartingales. Our main goal is to analyze the issue of replication of a generic contingent claim using a selffinancing trading strategy that is additionally subject to an algebraic constraint, referred to as
Utility valuation of credit derivatives and application to CDOs
 In preparation
, 2006
"... We study the impact of riskaversion on the valuation of credit derivatives. Using the technology of utilityindifference pricing in intensitybased models of default risk, we analyze resulting yield spreads in both simple singlename credit derivatives, and complex multiname securities, particular ..."
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Cited by 9 (2 self)
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We study the impact of riskaversion on the valuation of credit derivatives. Using the technology of utilityindifference pricing in intensitybased models of default risk, we analyze resulting yield spreads in both simple singlename credit derivatives, and complex multiname securities, particularly CDOs. We introduce the diversity coefficient that characterizes the effects of defaultable investment opportunities. The impact of riskaverse valuation on CDO tranche spreads is also expressed in terms of implied
Utility valuation of multiname credit derivatives and application to CDOs
, 2008
"... We study the impact of riskaversion on the valuation of credit derivatives. Using the technology of utilityindifference pricing in intensitybased models of default risk, we analyze resulting yield spreads in multiname credit derivatives, particularly CDOs. We study first the idealized problem wit ..."
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Cited by 7 (2 self)
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We study the impact of riskaversion on the valuation of credit derivatives. Using the technology of utilityindifference pricing in intensitybased models of default risk, we analyze resulting yield spreads in multiname credit derivatives, particularly CDOs. We study first the idealized problem with constant intensities where solutions are essentially explicit. We also give the large portfolio asymptotics for this problem. We then analyze the case where the firms have stochastic default intensities driven by a common factor, which can be viewed as another extreme from the independent case. This involves the numerical solution of a system of reactiondiffusion PDEs. We observe that the nonlinearity of the utilityindifference valuation mechanism enhances the effective correlation between the times of the credit events of the various firms leading to nontrivial senior tranche spreads, as often seen from market data.
2004b) Completeness of a reducedform credit risk model with discontinuous asset prices. Working paper
"... The goal of this work is to examine the issue of attainability of a generic defaultable claim within the reducedform approach to credit risk modelling, and the closely related issue of completeness of a credit risk model. In contrast to our previous work Bielecki et al. (2004a), we consider here th ..."
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Cited by 7 (6 self)
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The goal of this work is to examine the issue of attainability of a generic defaultable claim within the reducedform approach to credit risk modelling, and the closely related issue of completeness of a credit risk model. In contrast to our previous work Bielecki et al. (2004a), we consider here the case where the prices of defaultfree assets and the predefault values of defaultable assets follow
Systematic equitybased credit risk: a CEV model with jump to default
 Journal of Economic Dynamics and Control
, 2009
"... to Default ..."