The Art of Credit Derivatives: Demystifying the Black Swan

9

Pricing Synthetic CDO Tranches

The finest thought runs the risk of being irrevocably forgotten if it is not written down.

Arthur Schopenhauer

9.1 INTRODUCTION

Since the introduction of the 1-factor Gaussian copula model for pricing synthetic Collateralized Debt Obligation (CDO) tranches by Andersen et al. (2003), correlation is seen as an exogenous parameter used to match observed market quotes. First the market adopted the concept of implied compound correlation. In tandem with the concept of volatility in the Black-Scholes option pricing framework, compound correlation was the parameter to be put in the model to match observed market prices of tranches.

One of the problems of this approach resides in its unsuitability for interpolation. We have seen in the last chapter that the standard attachment points are 3%, 6%, 9%, 12% and 22% for iTraxx Europe Main and 3%, 7%, 10%, 15% and 30% for CDX.NA.IG. Given the implied compound correlations for the [3%-6%] and [6%-9%] tranches of iTraxx Europe Main it is not clear which value to use for a nonstandard tranche such as, e.g. [5%-8%]. Besides the problems of interpolation we can also mention that during some market events correlation may receive non-meaningful values (e.g. during the auto crisis of May 2005).

The current widespread market approach is to use the concept of base correlation (BC) introduced by McGinty et al. (2004). In the base correlation methodology only equity or base tranches are defined, where base or equity ...