Inside the CDO Correlation Surface
38th Conference on Stochastic Processes and their Applications, Oxford, UK
Posted: 2 May 2014 Last revised: 17 Apr 2018
Date Written: July 1, 2015
No-arbitrage surfaces implied from the parameters of benchmark stochastic financial models have attracted considerable attention. They are convenient objects that statically give access to the marginals of the state variables and dynamically to their law. The former help to price vanillas and to detect arbitrage in a model-free way, the latter to properly hedge and price exotics. For equity derivatives such research has made significant advances recently. Strikingly, for portfolio credit derivatives it is missing. The purpose of the paper is to provide such. We employ the particular property of the CDO swap that as a complex instrument it has simultaneously a convex pay-off on the total portfolio loss, is characterized by intensity with the loss being bounded and increasing, and is dependent on the sum of the individual losses of the reference entities. In this way, it shares the characteristics of an equity derivative, a fixed income security, and a financial portfolio respectively. We use all that to give a characterization of the correlation surface the CDO market implies, its asymptotics, and basic dynamic properties.
Keywords: CDO, correlation, compensator, term structure, portfolio
JEL Classification: G13
Suggested Citation: Suggested Citation