Dynamic hedging of portfolio credit risk in a Markov copula model. (English) Zbl 1295.91096
Summary: 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.
MSC:
| 91G40 | Credit risk |
| 91G10 | Portfolio theory |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
Keywords:
portfolio credit risk; credit derivatives; Markov copula model; common shocks; dynamic hedgingReferences:
| [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) · Zbl 1314.91223 |
| [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) · Zbl 1314.91224 |
| [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) · Zbl 1302.91184 |
| [4] | Bielecki, T.R., Crépey, S., Jeanblanc, M.: Up and down credit risk. Quant. Finance 10(10), 1137-1151 (2010) · Zbl 1201.91212 · doi:10.1080/14697680903382776 |
| [5] | Assefa, S.; Bielecki, T. R.; Crépey, S.; Jeanblanc, M.; Bielecki, T. R. (ed.); Brigo, D. (ed.); Patras, F. (ed.), CVA computation for counterparty risk assessment in credit portfolios, 397-436 (2011), New York |
| [6] | Bielecki, T.R., Crépey, S., Jeanblanc, M., Zargari, B.: Valuation and hedging of CDS counterparty exposure in a Markov copula model. Int. J. Theor. Appl. Finance 15(1), 1250004 (2012) · Zbl 1243.91100 · doi:10.1142/S0219024911006498 |
| [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) · Zbl 1290.91178 |
| [8] | Elouerkhaoui, Y.: Pricing and hedging in a dynamic credit model. Int. J. Theor. Appl. Finance 10(4), 703-731 (2007) · Zbl 1291.91223 · doi:10.1142/S0219024907004408 |
| [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) |
| [10] | Brigo, D., Pallavicini, A., Torresetti, R.: Cluster-based extension of the generalized Poisson loss dynamics and consistency with single names. Int. J. Theor. Appl. Finance 10(4), 607-632 (2007) · Zbl 1291.91243 · doi:10.1142/S0219024907004342 |
| [11] | Lindskog, F., McNeil, A.J.: Common Poisson shock models: applications to insurance and credit risk modelling. ASTIN Bull. 33(2), 209-238 (2003) · Zbl 1087.91030 · doi:10.2143/AST.33.2.503691 |
| [12] | Marshall, A., Olkin, I.: A multivariate exponential distribution. J. Am. Stat. Assoc. 2, 84-98 (1967) · Zbl 0147.38106 |
| [13] | Bielecki, T. R.; Jakubowski, J.; Niewȩglowski, M., Dynamic modeling of dependence in finance via copulae between stochastic processes, No. 198, 33-76 (2010) · doi:10.1007/978-3-642-12465-5_2 |
| [14] | Crépey, S., Jeanblanc, M., Wu, D.L.: Informationally dynamized Gaussian copula. Int. J. Theor. Appl. Financ. 16(2) (2013). doi:10.1142/S0219024913500088 · Zbl 1266.91119 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
