The modeling of extreme stochastic dependence using copulas and extreme value theory: case study from energy prices

Abstract

In this paper, we investigate the properties of tail dependence with an approach which is based on the copula models and extreme value theory to obtain a joint distribution function of extreme events and to quantify the dependence between random variables. To achieve this objective, we quantify the large co-movements between the random variables returns which are based on the data set daily quotes of exceeds the threshold value of random variables. In this study, stochastic dependence was modeled by the copulas which it provides a good approach for constructing multivariate probability distributions with flexible marginal’s and different forms of dependence. Choosing the right copula is very important in modeling. The multivariate distributions are easily simulated using the copulas. Finally we can describe the copula family which correctly represents the dependence. To demonstrate the usefulness of the proposed models, we confine our analysis to big price changes of energy commodity spot prices. The empirical findings demonstrated that the copula model which is combined the extreme value theory is a good approach to model the together extreme large changes.