Data-driven and distribution-free estimation of tailed-related risks for GARCH models using composite asymmetric least squares regression

Abstract

In this paper, we propose a two-step procedure to estimate tail-related risks like VaR and ES for the GARCH model. We inventively put forward the composite asymmetric least squares (CALS) regression to estimate the volatility structure and distinguish it from the innovation process in the GARCH model. Then noting that expectile bridges the gap between VaR and ES, we introduce the empirical likelihood method to determine these relations. Accordingly, a new optimization algorithm is proposed. Compared with the existing grid-search method, this new proposed method is data-driven and distribution-free, and shares better estimation accuracy and computational efficiency. Monte Carlo simulation studies and empirical analysis also indicate that our proposed method is superior to some alternative existing tail-related risk estimation methods.