On break-even correlation: the way to price structured credit derivatives by replication
We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient conditions so that the corresponding asset prices are martingales and introduce the concept of "break-even" correlation matrix. When no sudden jump-to-default events occur, we show that the perfect replication of these payoffs under the GCM is obtained if and only if the underlying single name credit spreads follow a particular family of dynamics. We calculate the corresponding break-even correlations and we exhibit a class of Merton-style models that are consistent with this result. We explain why the GCM does not have a lot of competitors among the class of one-period static models, except perhaps the Clayton copula.
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- Merton, Robert C., 1973.
"On the pricing of corporate debt: the risk structure of interest rates,"
684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
- Rüdiger Frey & Jochen Backhaus, 2008. "Pricing And Hedging Of Portfolio Credit Derivatives With Interacting Default Intensities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 611-634.
- Damiano Brigo & Aurélien Alfonsi, 2005. "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model," Finance and Stochastics, Springer, vol. 9(1), pages 29-42, January.
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