Empirical analysis of price returns is an essential component of the development of valuation methods in any asset class. The design of hedging strategies, construction of investor index products, and model selection for derivatives valuation each rely heavily on statistical estimates of moments and models of returns processes. Energy commodities present some unique challenges: the effects of seasonality and inventory on covariance structure are significant; forward price volatility decays rapidly with tenor; returns are highly nonnormal. These features are juxtaposed on markets in which options liquidity is concentrated at short tenors and near the money, and trading activity in correlation products is minimal, constraining the availability of market-implied information about returns distributions.

A casual examination of forward prices shows that correlations in returns between different contracts of the same commodity can be quite high. Figure 5.1 shows several nearby price series for West Texas Intermediate (WTI); recall that the nth nearby contract is the nth contract currently trading. A nearby price series is the concatenation of a set of nearby prices across trading dates. Variations between the different prices are discernible, but the dominant feature is that these price series are tightly coupled, suggesting high correlations between price returns of the series of forward contracts. This is the case, as we will see shortly.