Looking for the right copula

It is widely accepted that the probability of a company defaulting on its debt is linked to the value of its assets, which can be inferred (not necessarily in a unique way) from its equity price. The intellectual argument is long established, and empirical research by KMV and others convincingly point to a predictive link – although long-term regression studies by Standard & Poor’s are less encouraging.

One naturally is led to argue that the valuation of products involving basketsof credits, such as single-tranche collateralised debt obligations, should bedetermined from the joint returns on a basket of assets, which in turn can beinferred from baskets of equities. For derivatives directly linked to equitybaskets, such as index options, the correlation between components implied bythe market can be directly compared with historical estimates, permitting a fairvaluation approach to these