Abstract

The recent financial crisis has revealed major shortcomings in the existing approaches for modeling credit derivatives. This dissertation studies various issues related to the modeling of credit deriva-tives: hedging of portfolio credit derivatives, calibration of dynamic credit models, and modeling of credit default swap portfolios. In the first part, we compare the performance of various hedging strategies for index collater-alized debt obligation (CDO) tranches during the recent financial crisis. Our empirical analysis shows evidence for market incompleteness: a large proportion of risk in the CDO tranches appears to be unhedgeable. We also show that, unlike what is commonly assumed, dynamic models do not necessarily perform better than static models, nor do high-dimensional bottom-up models perform better than simpler top-down models. On the other hand, model-free regression-based hedging appears to be surprisingly effective when compared to other hedging strategies. The second part is devoted to computational methods for constructing an arbitrage-free CDO pricing model compatible with observed CDO prices. This method makes use of an inversion formula for computing the aggregate default rate in a portfolio from expected tranche notionals, and a quadratic programming method for recovering expected tranche notionals from CDO spreads.