A Continuous Time GARCH Process Driven by a Lévy Process: Stationarity and Second Order Behaviour

Klüppelberg, Claudia; Lindner, Alexander M. und Maller, R. A. (2005): A Continuous Time GARCH Process Driven by a Lévy Process: Stationarity and Second Order Behaviour. Sonderforschungsbereich 386, Discussion Paper 425

Abstract

We use a discrete time analysis, giving necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, tosuggest an extension of the (G)ARCH concept to continuous time processes. Our "COGARCH" (continuous time GARCH) model, based on a single background driving Levy process, is different from, though related to, other continuous time stochastic volatility models that have been proposed. The model generalises the essential features of discrete time GARCH processes, and is amenable to further analysis, possessing useful Markovian and stationarity properties.

• Dokumententyp: Paper
• Fakultät: Mathematik, Informatik und Statistik > Statistik > Sonderforschungsbereich 386 ; Sonderforschungsbereiche > Sonderforschungsbereich 386
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch