Synthetic Collateralized Debt Obligations (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 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, and 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. Each model's underlying theoretical approach is commented upon and the computational complexity of each of the models is then described and analyzed. It is observed that there is a significant model and correlation risk in the credit derivatives market due to the discrepancies between the models in terms of hedging results and also due to the frequent changes in the tranches' behavior.
Index tranches offer the opportunity to trade correlation products through their standardized
form and liquidity. Tranched index products are similar in many respects to synthetic
Collateralized Debt Obligation (CDO) tranches. These products are exposed to defaults, spread1
movements, correlation and recovery uncertainties. Pricing and hedging2 index tranches
require advanced modeling and an understanding of the sensitivities of different tranches in
the capital structure to these sources of risk.
Synthetic CDOs have been the principal growth engine for the credit derivatives market over
the last few years. They create new, customized asset classes by allowing various investors to
share the risk and return of an underlying portfolio of Credit Default Swaps3 (CDS). Multiple
tranches of the underlying portfolio are issued, offering investors various maturity and credit
risk characteristics. Thus, the attractiveness to investors is determined by the underlying
portfolio of CDS and the rules for sharing the risk and return. A synthetic CDO is often called “a correlation product” because, in simple words, it is a contract that references the default
of more than one obligor. Investors in this product are buying correlation risk, or more exactly,
joint default risk between several obligors. The underlying portfolio loss distribution directly
determines the tranche cash flows and thus the tranche valuation.
|
