Klüppelberg, Claudia Lindner, Alexander M. Maller, Ross
Year of Publication:
Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 425
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 Léy 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.