Modeling Dependence with Copulas
Great spirits have always encountered violent opposition from mediocre minds.
In order to generate the joint loss distribution of a credit portfolio one needs a framework to express the dependency or correlation between the underlying references which may be either single name instruments or asset backed securities. In order to be usable in practice, the adopted approach should have a few desirable features. First, it needs to be as simple and easy to understand as possible. That is, error checking is not overly complex. Second, calibration to available market data should be tractable. There is no point in generating a loss distribution that one cannot relate to observable market data. Additionally, the adopted approach should be scalable, that is, applicable to a small portfolio involving a couple of references as well as to very large portfolios. Finally, the generated loss distribution for the whole portfolio has to be compatible with the marginal loss distributions of the underlying references. This needs to be so as in a liquid market the dynamics of one reference does not change because it is in the portfolio of a certain institution. If the last two conditions are not fulfilled coherence problems between the two loss distributions may be encountered when trying to hedge a single name or a subportfolio exposure within a larger portfolio.
In practice, the dependence relation within a portfolio is generated ...