Recent Advancements in the Theory and Practice of Credit Derivatives

In the Black-Cox model, a firm makes default when its value hits an exponential barrier. Here, we propose an hybrid model that generalizes this framework. The default intensity can take two different values and switches when the firm value crosses the barrier. Of course, the intensity level is higher below the barrier. We get an analytic formula for the Laplace transform of the default time and present numerical methods to get back its distribution. Last, we explain how this model can calibrate Credit Default Swap prices and show its tractability on different kind of data. Rama CONT, CNRS and Columbia University Dynamic hedging of portfolio credit derivatives Abstract. (With Yu Hang KAN, Columbia University). We study hedging of index CDO tranches with the underlying CDS contracts and the index in various aggregate loss models which account for default contagion and spread risk, using various top-down and bottom-up model specifications. Market incompleteness precludes perfect hedging and suggest comparing various strategies in terms of residual risk. In particular, we compare sensitivity-based hedging with hedging strategies based on quadratic risk minimization. Numerical results obtained in models calibrated to iTraxx and CDX market data reveal significant differences in the hedge ratios and show, unlike what had been previously suggested in the literature by comparing copula-based models, that hedging strategies are subject to substantial model risk. Finally, we perform an empirical comparison of hedging performance using ITRAXX and CDX time series. Our study reveals in particular that -hedging with the index in a top-down model may outperform hedging with individual CDS in a bottom-up models delta-hedging of spread risk using a Gaussian Copula model does not appear to be an effective hedging strategy, especially after the onset of subprime crisis. This talk is based on: R Cont, R Deguest, Y.H, Kan (2009) Default Intensities implied by CDO Spreads: Inversion Formula and Model Calibration, http://ssrn.com/abstract=1447979 R Cont, Y.H. Kan (2008) Dynamic hedging of credit derivatives, http://ssrn.com/abstract=1349847 R Cont, A Minca (2008) Recovering portfolio default intensities implied by CDO tranches, http://ssrn.com/abstract=1104855 (With Yu Hang KAN, Columbia University). We study hedging of index CDO tranches with the underlying CDS contracts and the index in various aggregate loss models which account for default contagion and spread risk, using various top-down and bottom-up model specifications. Market incompleteness precludes perfect hedging and suggest comparing various strategies in terms of residual risk. In particular, we compare sensitivity-based hedging with hedging strategies based on quadratic risk minimization. Numerical results obtained in models calibrated to iTraxx and CDX market data reveal significant differences in the hedge ratios and show, unlike what had been previously suggested in the literature by comparing copula-based models, that hedging strategies are subject to substantial model risk. Finally, we perform an empirical comparison of hedging performance using ITRAXX and CDX time series. Our study reveals in particular that -hedging with the index in a top-down model may outperform hedging with individual CDS in a bottom-up models delta-hedging of spread risk using a Gaussian Copula model does not appear to be an effective hedging strategy, especially after the onset of subprime crisis. This talk is based on: R Cont, R Deguest, Y.H, Kan (2009) Default Intensities implied by CDO Spreads: Inversion Formula and Model Calibration, http://ssrn.com/abstract=1447979 R Cont, Y.H. Kan (2008) Dynamic hedging of credit derivatives, http://ssrn.com/abstract=1349847 R Cont, A Minca (2008) Recovering portfolio default intensities implied by CDO tranches, http://ssrn.com/abstract=1104855 Areski Cousin, ISFA, Université de Lyon Dynamic hedging of CDO tranches in Markovian contagion models