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

Claudia Klüppelberg, Alexander Lindner, Ross Maller

Research output: Contribution to journalArticlepeer-review

137 Scopus citations

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 languageEnglish
Pages (from-to)601-622
Number of pages22
JournalJournal of Applied Probability
Volume41
Issue number3
DOIs
StatePublished - Sep 2004

Keywords

  • ARCH model
  • Conditional heteroscedasticity
  • GARCH model
  • Lévy process
  • Perpetuities
  • Stability
  • Stationarity
  • Stochastic integration

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