A Continuous Time GARCH Process Driven by a Lévy Process: Stationarity and Second Order Behaviour
نویسنده
چکیده
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, to suggest an extension of the (G)ARCH concept to continuous time processes. Our “COGARCH” (continuous time GARCH) model, based on a single background driving Lévy 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. AMS 2000 Subject Classifications: primary: 60G10, 60J25, 91B70 secondary: 91B28, 91B84
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