Forecasting Dependent Tail Value-at-Risk by ARMA-GJR-GARCH-Copula Method and Its Application in Energy Risk - Josaphat, Bony Parulian (IndoMS, 2023)
One widely known risk measure is Tail Value-at-Risk (TVaR), which isthe average of the values of random risk that exceed the Value-at-Risk (VaR). Thisclassic risk measure of TVaR does not take into account the excess of another randomrisk (associated risk) that may have an effect on target risk. Copula function expresses a methodology that represents the dependence structure of random variablesand 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-GARCHmodel, this article argues a novel approach, called ARMA-GJR-GARCH-copulawith Monte Carlo method, to calculate the DTVaR of dependent energy risks. Thiswork shows an implementation of the ARMA-GJR-GARCH-copula model in forecasting the DTVaR of energy risks of NYH Gasoline and Heating oil associated withenergy risk of WTI Crude oil. The empirical results demonstrate that, the simplerGARCH-Clayton copula is better in forecasting DTVaR of Gasoline energy risk thanthe MA-GJR-GARCH-Clayton copula. On the other hand, the more complicatedMA-GJR-GARCH-Frank copula is better in forecasting DTVaR of Heating oil energy risk than the GARCH-Frank copula. In this context, energy sector marketplayers should invest in Heating oil because the DTVaR forecast of Heating oil ismore accurate than that of Gasoline.