A continuous-time GARCH process driven by a levy process: Stationarity and second-order behaviour

Claudia Klüppelberg; Alexander Lindner; Ross Maller

doi:10.1239/jap/1091543413

A continuous-time GARCH process driven by a levy process: Stationarity and second-order behaviour

Claudia Klüppelberg^*, Alexander Lindner, Ross Maller

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

148 Citations (Scopus)

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, 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.

Original language	English
Pages (from-to)	601-622
Number of pages	22
Journal	Journal of Applied Probability
Volume	41
Issue number	3
DOIs	https://doi.org/10.1239/jap/1091543413
Publication status	Published - Sept 2004

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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, 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 L{\'e}vy 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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KW - ARCH model

KW - Conditional heteroscedasticity

KW - GARCH model

KW - Lévy process

KW - Perpetuities

KW - Stability

KW - Stationarity

KW - Stochastic integration

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JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 3

ER -

A continuous-time GARCH process driven by a levy process: Stationarity and second-order behaviour

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