| 1. |
- Bielecki, Tomasz R., et al.
(författare)
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A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part I: Markov Copula Perspective
- 2014
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Ingår i: Recent Advances in Financial Engineering 2012. - New Jersey London Hong Kong : World Scientific. - 9789814571630 ; , s. 25-49
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Bokkapitel (refereegranskat)abstract
- We consider a bottom-up Markovian copula model of portfolio credit risk where instantaneous contagion is possible in the form of simultaneous defaults. Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static copula set-up. In this sense this model solves the bottom-up top-down puzzle which the CDO industry had been trying to do for a long time. It can be applied to any dynamic credit issue like consistent valuation and hedging of CDSs, CDOs and counterparty risk on credit portfolios.
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| 2. |
- Bielecki, Tomasz R., et al.
(författare)
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A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part II: Common-Shock Interpretation, Calibration and Hedging Issues
- 2014
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Ingår i: Recent Advances in Financial Engineering 2012. - New Jersey London Hong Kong : World Scientific. - 9789814571630 ; , s. 51-73
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Bokkapitel (refereegranskat)abstract
- In this paper, we prove that the conditional dependence structure of default times in the Markov model of [4] belongs to the class of Marshall- Olkin copulas. This allows us to derive a factor representation in terms of “common-shocks”, the latter beeing able to trigger simultaneous defaults in some pre-specified groups of obligors. This representation depends on the current default state of the credit portfolio so that fast convolution pricing schemes can be exploited for pricing and hedging credit portfolio derivatives. As emphasized in [4], the innovative breakthrough of this dynamic bottom-up model is a suitable decoupling property between the dependence structure and the default marginals as in [10] (like in static copula models but here in a full-flesh dynamic “Markov copula” model). Given the fast deterministic pricing schemes of the present paper, the model can then be jointly calibrated to single-name and portfolio data in two steps, as opposed to a global joint optimization procedures involving all the model parameters at the same time which would be untractable numerically. We illustrate this numerically by results of calibration against market data from CDO tranches as well as individual CDS spreads. We also discuss hedging sensitivities computed in the models thus calibrated.
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| 3. |
- Bielecki, Tomasz R., et al.
(författare)
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A Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries
- 2014
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Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 43:7, s. 1362-1389
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Tidskriftsartikel (refereegranskat)abstract
- In Bielecki et al. (2014a), the authors introduced a Markov copula model of portfolio credit risk where pricing and hedging can be done in a sound theoretical and practical way. Further theoretical backgrounds and practical details are developed in Bielecki et al. (2014b,c) where numerical illustrations assumed deterministic intensities and constant recoveries. In the present paper, we show how to incorporate stochastic default intensities and random recoveries in the bottom-up modeling framework of Bielecki et al. (2014a) while preserving numerical tractability. These two features are of primary importance for applications like CVA computations on credit derivatives (Assefa et al., 2011; Bielecki et al., 2012), as CVA is sensitive to the stochastic nature of credit spreads and random recoveries allow to achieve satisfactory calibration even for “badly behaved” data sets. This article is thus a complement to Bielecki et al. (2014a), Bielecki et al. (2014b) and Bielecki et al. (2014c).
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| 4. |
- Bielecki, Tomasz R., et al.
(författare)
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A Markov Copula Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In [4], the authors introduced a Markov copula model of portfolio credit risk. This model solves the top-down versus bottom-up puzzle in achieving efficient joint calibration to single-name CDS and to multi-name CDO tranches data. In [4], we studied a general model, that allows for stochastic default intensities and for random recoveries, and we conducted empirical study of our model using both deterministic and stochastic default intensities, as well as deterministic and random recoveries only. Since, in case of some “badly behaved” data sets a satisfactory calibration accuracy can only be achieved through the use of random recoveries, and, since for important applications, such as CVA computations for credit derivatives, the use of stochastic intensities is advocated by practitioners, efficient implementation of our model that would account for these two issues is very important. However, the details behind the implementation of the loss distribution in the case with random recoveries were not provided in [4]. Neither were the details on the stochastic default intensities given there. This paper is thus a complement to [4], with a focus on a detailed description of the methodology that we used so to implement these two model features: random recoveries and stochastic intensities.
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| 5. |
- Bielecki, Tomasz R., et al.
(författare)
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Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model
- 2014
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 0022-3239 .- 1573-2878. ; 161:1, s. 90-102
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Tidskriftsartikel (refereegranskat)abstract
- We devise a bottom-up dynamic model of portfolio credit risk where instantaneous contagion is represented by the possibility of simultaneous defaults. Due to a Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-step procedure, much like in a standard static copula setup. In this sense this solves the bottom-up top-down puzzle which the CDO industry had been trying to do for a long time. This model can be used for any dynamic portfolio credit risk issue, such as dynamic hedging of CDOs by CDSs, or CVA computations on credit portfolios.
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| 6. |
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