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

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  • 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.

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Handle: RePEc:rsk:journ4:2161017
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