Dependency Modeling

As should be quite clear to this stage, the need to understand the joint dependence between multiple stochastic entities is of critical importance in energy markets. We have of course considered numerous examples in the context of spread-option structures, where the relevant measure of dependence in Gaussian scenarios is correlation.1 We have also considered some fairly rich classes of canonical processes that extend the standard Gaussian framework (affine jump diffusions and Lévy processes). In addition, we examined the interplay between short-term co-movements and long-term stationarity through cointegration analysis. We now examine another concept useful for modeling joint structure, namely, copulas. As will be seen, an interesting facet of copulas is the ability to construct joint dependency in terms of specified marginal distributions. To the extent that marginal distributions may often be extracted from market information (through, say, option prices), the flexibility offered by copula-based models can be quite enticing. Not surprisingly, there is a voluminous literature available, including book-length treatments by Nelsen (1999) and detailed survey articles in Embrechts et al. (2002, 2003). Our objective here is to provide an overview and highlight the most promising directions as they pertain to energy modeling.