Base Correlation Mapping
A goal without a plan is just a wish.
Antoine de Saint-Exupery
In Chapter 9 we introduced the recursive approach for pricing synthetic CDO tranches developed by Andersen et al. (2003). We have seen that for pricing the tranches the exogenous correlation plays a crucial role. We showed that the market adopted first the concept of implied compound correlation and that a crucial problem of this approach resided in its unsuitability for interpolation when pricing nonstandard tranches. The concept of base correlation (BC) introduced by McGinty et al. (2004) solved the problems that implied compound correlation could not. We saw that in the base correlation methodology only equity or base tranches (with attachment point 0) are considered. The price of a tranche [A-D] is calculated using the two equity tranches with A and D as detachment points. Additionally, we showed the algorithm using both the Gaussian and Lévy frameworks. The BC concept became widely used and is supposed to be suitable for interpolation both for nonstandardized tranches and for bespoke portfolios.
In Chapter 10 we have shown results of historical tests involving Gaussian and Lévy base correlation. Problems of the base correlation approach have been addressed in Chapter 11. By comparing Figures 11.2 and 11.3 we have shown that the concept of expected loss is much more appealing to intuition than the concept of base correlation. In that chapter we presented the concept ...