TY - JOUR
T1 - A continuous-time GARCH process driven by a levy process
T2 - Stationarity and second-order behaviour
AU - Klüppelberg, Claudia
AU - Lindner, Alexander
AU - Maller, Ross
PY - 2004/9
Y1 - 2004/9
N2 - 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 ARCH and GARCH concepts 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.
AB - 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 ARCH and GARCH concepts 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.
KW - ARCH model
KW - Conditional heteroscedasticity
KW - GARCH model
KW - Lévy process
KW - Perpetuities
KW - Stability
KW - Stationarity
KW - Stochastic integration
UR - http://www.scopus.com/inward/record.url?scp=10244257719&partnerID=8YFLogxK
U2 - 10.1239/jap/1091543413
DO - 10.1239/jap/1091543413
M3 - Article
AN - SCOPUS:10244257719
SN - 0021-9002
VL - 41
SP - 601
EP - 622
JO - Journal of Applied Probability
JF - Journal of Applied Probability
IS - 3
ER -