Liquidity-adjusted value-at-risk using extreme value theory and copula approach

Abstract

In this study, we propose the application of the GARCH-EVT-Copula model in estimating liquidity-adjusted value-at-risk (L-VaR) of energy stocks while modeling nonlinear dependence between return and bid-ask spread. Using the L-VaR framework of Bangia et al. (1998), we present a more parsimonious model that effectively captures non-zero skewness, excess kurtosis, and volatility clustering of both return and spread distributions of energy stocks. Moreover, to measure the nonlinear dependence between return and spread series, we use multiple copulas: Clayton, Gumbel, Frank, Normal, and Student-t. Based on the statistical backtesting and economic loss functions, our results suggest that the GARCH-EVT-Clayton copula is superior and most consistent in forecasting L-VaR compared with other competing models. This finding has several implications for investors, market makers, and daily traders who appreciate the importance of liquidity in market risk computation.