Multi-period conditional distribution functions for heteroscedastic models with applications to VaR.

Raymond Brummelhuis (1) , Dominique Guegan (2)

1 Birckbeck College
2 IDHE - Institutions et Dynamiques Historiques de l'Economie

For a GARCH(1,1) process, we study the large deviation asymptotics at the horizon k and their consequences for extreme quantile estimation. The results are relevant for the estimation of multi-period Value at Risk and prove that the heuristic “square k” rule used in financial risk management is false in the context of GARCH processes.

Mots clés: GARCH models; Large deviation probabilities; Laplace integrals; Value at risk; Value at risk.

Domaines: Economies et finances; Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Raymond Brummelhuis, Dominique Guegan. Multi-period conditional distribution functions for heteroscedastic models with applications to VaR.. Journal of Applied Probability, 2005, 42 (2), pp.35-55. ⟨halshs-00179336⟩