A Continuous Time GARCH Process Driven by a Lévy Process: Stationarity and Second Order Behaviour
Beschreibung
vor 19 Jahren
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.
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.
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