Semiparametric GARCH Models with Long Memory Applied to Value at Risk and Expected Shortfall

Abstract

In this paper new semiparametric GARCH models with long memory are introduced.
A multiplicative decomposition of the volatility into a conditional and unconditional
component is assumed. The estimation of the latter is carried out by means of a
data-driven local polynomial smoother. Recurring on the revised recommendations
by the Basel Committee 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 (VaR) 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 to that, 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 to their
conventional, parametric counterparts.

Keywords: semiparametric, long memory, GARCH models, forecasting, Value at Risk, Expected Shortfall, traffic light test, Basel Committee on Banking Supervision

JEL Classification: C14, C51, C52, G17, G32