Hedging of Defaultable Claims

Bielecki, Tomasz R.; Jeanblanc, Monique; Rutkowski, Marek

doi:10.1007/978-3-540-44468-8_1

Cited by 70 publications

(64 citation statements)

References 43 publications

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“…For recent applications of indifference pricing to credit risk, see also Collin-Dufresne and Hugonnier [6], Bielecki et al [3,4], and Shouda [30]. Analysis of the single-and two-name cases appears in our previous work [31].…”

Section: Credit Derivativesmentioning

confidence: 99%

“…Here we restrict to the special class of doubly stochastic default times that may be correlated only through their intensity processes. For more general constructions of default times, and technical details on intensities, we refer, for instance, to [4]. As is common in credit applications, we suppose the filtration (F t ) is generated by some factor process Y .…”

Section: General Modelmentioning

confidence: 99%

“…The value function for n = 0 is given by (4). The market information is contained in the coefficients D(I k n ), E(I k n ) and F (I k n ).…”

Section: Maximal Expected Utility Problemmentioning

confidence: 99%

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Utility valuation of multi-name credit derivatives and application to CDOs

Sircar

Zariphopoulou

2009

Quantitative Finance

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We study the impact of risk-aversion on the valuation of credit derivatives. Using the technology of utility-indifference pricing in intensity-based 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 reaction-diffusion PDEs. We observe that the nonlinearity of the utility-indifference valuation mechanism enhances the effective correlation between the times of the credit events of the various firms leading to non-trivial senior tranche spreads, as often seen from market data.

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Section: Credit Derivativesmentioning

confidence: 99%

Section: General Modelmentioning

confidence: 99%

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Utility valuation of multi-name credit derivatives and application to CDOs

Sircar

Zariphopoulou

2009

Quantitative Finance

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“…Let us mention in this regard that in a companion paper by Bielecki et al [1] we also include defaultable assets in our portfolio, and we show how to use constrained portfolios to derive replicating strategies for defaultable contingent claims (e.g., credit derivatives). The reader is also referred to Bielecki et al [1], where the case of continuous semimartingale markets was studied, for some background information regarding the probabilistic and financial set-up, as well as the terminology used in this note.…”

Section: Introductionmentioning

confidence: 99%

“…The reader is also referred to Bielecki et al [1], where the case of continuous semimartingale markets was studied, for some background information regarding the probabilistic and financial set-up, as well as the terminology used in this note. The main emphasis is put here on the relationship between completeness of a security market model with unconstrained trading and completeness of an associated model in which only trading strategies satisfying the balance condition are allowed.…”

Section: Introductionmentioning

confidence: 99%