Copulas: A new technique to model dependence in petroleum decision making

Abstract

A key step in valuing petroleum investment opportunities is to construct a model that portrays the uncertainty inherent in the investment decision. In almost all such cases, several of the random variables that are relevant for the model are correlated. Properly accounting for and modelling these correlations is essential in deriving reliable valuations for decision support. The Envelope method and the Iman–Conover method are popular approaches to model dependency in the petroleum industry. Although these models work well in many cases, there are situations where they fail to accurately account for important characteristics of the correlations. In many cases the structure of the dependence between two random variables is important. The approaches typically used to model dependence in oil and gas evaluations often fail to address the dependence structure. The copulas technique, which is well known in financial risk management and insurance applications, has proven to be a superior tool for modelling dependency structures. Yet, to our knowledge, it has rarely been used in petroleum applications. A copula is a statistical concept that relates random variables. It is a function that links the marginal distributions to the joint distribution. A copula can model the dependence structure given any type of marginal distribution, which is not possible with other correlation measures. This is illustrated by the fact that the copula approach is able to separate the marginal distribution from the correlation. The objective of this paper is to illustrate the potential benefits of using copulas to model dependencies in oil and gas applications with a particular focus on the reserves problem. This paper introduces the copulas method and then compares and contrasts it with some of the more commonly used approaches to model dependence. We then show that the traditional methods have problems in accurately revealing the dependence structure in the tails of the variable distributions. Finally, we illustrate how the dependence structure can be captured and modelled using the copulas approach.