Forecasting Dependent Tail Value-at-Risk by ARMA-GJR-GARCH-Copula Method and Its Application in Energy Risk

Abstract

One widely known risk measure is Tail Value-at-Risk (TVaR), which is
the average of the values of random risk that exceed the Value-at-Risk (VaR). This
classic risk measure of TVaR does not take into account the excess of another random
risk (associated risk) that may have an effect on target risk. Copula function expresses a methodology that represents the dependence structure of random variables
and has been used to create a risk measure of Dependent Tail Value-at-Risk (DTVaR). Incorporating copula into the forecast function of the ARMA-GJR-GARCH
model, this article argues a novel approach, called ARMA-GJR-GARCH-copula
with Monte Carlo method, to calculate the DTVaR of dependent energy risks. This
work shows an implementation of the ARMA-GJR-GARCH-copula model in forecasting the DTVaR of energy risks of NYH Gasoline and Heating oil associated with
energy risk of WTI Crude oil. The empirical results demonstrate that, the simpler
GARCH-Clayton copula is better in forecasting DTVaR of Gasoline energy risk than
the MA-GJR-GARCH-Clayton copula. On the other hand, the more complicated
MA-GJR-GARCH-Frank copula is better in forecasting DTVaR of Heating oil energy risk than the GARCH-Frank copula. In this context, energy sector market
players should invest in Heating oil because the DTVaR forecast of Heating oil is
more accurate than that of Gasoline.