Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model
- 788 Downloads
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.
KeywordsPortfolio credit risk Credit derivatives Markov copula model Common shocks Dynamic hedging
The research of T.R. Bielecki was supported by NSF Grant DMS–0604789 and NSF Grant DMS–0908099. The research of A. Cousin benefitted from the support of the DGE, the ANR project Ast&Risk and the “Chaire Management de la Modélisation”. The research of S. Crépey benefitted from the support of the “Chaire Risque de Crédit” and of the “Chaire Marchés en Mutation”, Fédération Bancaire Française. The research of A. Herbertsson was supported by the Jan Wallander and Tom Hedelius Foundation and by Vinnova.
- 1.Bielecki, T.R., Cousin, A., Crépey, S., Herbertsson, A.: A bottom-up dynamic model of portfolio credit risk—Part I: Markov copula perspective. Forthcoming in Recent Advances in Financial Engineering 2012, World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.1844574)
- 2.Bielecki, T.R., Cousin, A., Crépey, S., Herbertsson, A.: A bottom-up dynamic model of portfolio credit risk—Part II: Common-shock interpretation, calibration and hedging issues. Forthcoming in Recent Advances in Financial Engineering 2012, World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.2245130)
- 3.Bielecki, T.R., Cousin, A., Crépey, S., Herbertsson, A.: A bottom-up dynamic model of portfolio credit risk with stochastic intensities and random recoveries. Submitted (preprint version available at http://dx.doi.org/10.2139/ssrn.2159279)
- 5.Assefa, S., Bielecki, T.R., Crépey, S., Jeanblanc, M.: CVA computation for counterparty risk assessment in credit portfolios. In: Bielecki, T.R., Brigo, D., Patras, F. (eds.) Credit Risk Frontiers, pp. 397–436. Wiley, New York (2011) Google Scholar
- 7.Crépey, S., Rahal, A.: Simulation/regression pricing schemes for CVA computations on CDO tranches. Submitted (preprint version available at http://dx.doi.org/10.2139/ssrn.2242052)
- 9.Brigo, D., Pallavicini, A., Torresetti, R.: Credit models and the crisis: default cluster dynamics and the generalized Poisson loss model. J. Credit Risk 6(4), 39–81 (2010) Google Scholar
- 14.Crépey, S., Jeanblanc, M., Wu, D.L.: Informationally dynamized Gaussian copula. Int. J. Theor. Appl. Financ. 16(2) (2013). doi: 10.1142/S0219024913500088