Hedging Tranched Index Products: Illustration of the Model Dependency
20 Pages Posted: 11 May 2006
Date Written: April 2006
Synthetic CDOs have been the principal growth engine for the credit derivatives market over the last few years. The appearance of credit indices has helped the development of a more transparent and efficient market in correlation. This increase in volumes makes it necessary to use models of increasing diversity and complexity in order to model credit variables. Tranched index products are exposed to spread movements, defaults, correlation and recovery uncertainties. Hedging these risks requires an understanding of the sensitivities of the different tranches in the capital structure to these sources of risk. The dynamic hedging of index tranches presents dealers with two main challenges. First, the dealer must calculate the hedge positions (delta or hedge ratio) of the index or individual CDS or other index tranches. These deltas or hedge ratios are model-dependent, which leaves dealers with model risk. Second, the value of an index tranche depends on the correlation assumption used to price and hedge it. Since default correlation is unobservable, a dealer is exposed to the risk that his correlation assumption is wrong (correlation risk). In this paper, index tranches' properties and several hedging strategies are discussed. Next, the model risk and correlation risk are analyzed through the study of the efficiency of several factor-based copula models (like the Gaussian, the double-t and the double-NIG using implied correlation and a particular NIG one-factor model using historical correlation) versus historical data in terms of hedging capabilities. We comment on each model's underlying theoretical approach and then describe and analyze their computational complexity. We show that there is significant model and correlation risk in the credit derivatives market due to the discrepancies between models in terms of hedging results and to the frequent change in the tranches' behavior.
Keywords: CDO, Hedging, Index tranches, Delta, Hedge ratio, Model dependency, Correlation, Correlation smile, Factor models, NIG
JEL Classification: G12, G13
Suggested Citation: Suggested Citation