Semiparametric GARCH models with long memory applied to value-at-risk and expected shortfall

Sebastian Letmathe, Yuanhua Feng and André Uhde

Abstract

In this paper new semiparametric generalized autoregressive conditional heteroscedasticity (GARCH) models with long memory are introduced. A multiplicative decomposition of the volatility into a conditional component and an unconditional component is assumed. The estimation of the latter is carried out by means of a data-driven local polynomial smoother. According to the revised recommendations by the Basel Committee on Banking Supervision to measure market risk in the banks’ trading books, these new semiparametric GARCH models are applied to obtain rolling one-step ahead forecasts for the value-at-risk and expected shortfall (ES) for market risk assets. Standard regulatory traffic-light tests and a newly introduced traffic-light test for the ES are carried out for all models. In addition, model performance is assessed via a recently introduced model selection criterion. The practical relevance of our proposal is demonstrated by a comparative study. Our results indicate that semiparametric long-memory GARCH models are a meaningful substitute for their conventional, parametric counterparts.