Time-scaling of value-at-risk in GARCH(1,1) and AR(1)–GARCH(1,1) processes

Raymond Brummelhuis and Roger Kaufmann

Abstract

ABSTRACT

This paper investigates the estimation of a 10-day value-at-risk (VaR) based on a data set of 250 daily values. The commonly used square-rootof-time rule, which scales the one-day 99% VaR with a factor √10, is compared with alternative 10-day estimators in the case of random walks, GARCH(1,1) and AR(1)-GARCH(1,1) processes. Additionally, some theoretical results on N-day VaR in such models are presented. The overall conclusion is that, although not perfect, the √10-rule performs reasonably well.