Pricing and Hedging of Structured Credit Derivatives

Summary

Closed-form solutions are the Holy Grail in derivative pricing. We provide such pricing formulas for structured credit derivatives such as first- and k-th-to-default baskets as well as all kinds of tranches of collateralized debt obligations. First, we employ the conditional independence framework to derive semi-explicit pricing formulas for basket credit default swaps. Second, by introducing a linear factor model for individual hazard rates we obtain pricing formulas in terms of the moment-generating functions of the risk factors. We show how to calibrate this factor model to market data, especially to time series of credit spreads. Thus we distinguish between exogenous and endogenous modelling. For the cases of explicitly given moment-generating functions the pricing formulas become explicit.

This approach is characterized by its great flexibility and easy calibration to observed market data and leads to an efficient pricing by analytical calculation. In particular, our approach eases the calculation of hedge ratios for dynamic hedges of basket credit default swaps (also known as single-tranche technology or correlation trading) and other complex trading strategies.