Quantitative Modeling of Credit Derivatives

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 derivatives: 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 collateralized 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. Comparing this approach to other calibration methods, we find that model-dependent quantities such as the forward starting tranche spreads and jump-to-default ratios are quite sensitive to the calibration method used, even within the same model class. The last chapter of this dissertation focuses on statistical modeling of credit default swaps (CDSs). We undertake a systematic study of the univariate and multivariate properties of CDS spreads, using time series of the CDX Investment Grade index constituents from 2005 to 2009. We then propose a heavy-tailed multivariate time series model for CDS spreads that captures these properties. Our model can be used as a framework for measuring and managing the risk of CDS portfolios, and is shown to have better performance than the affine jump-diffusion or random walk models for predicting loss quantiles of various CDS portfolios.