COGARCH as a continuous-time limit of GARCH(1,1)

Jan Kallsen and Bernhard Vesenmayer

Stochastic Processes and their Applications, 2009, vol. 119, issue 1, 74-98

Abstract: COGARCH is an extension of the GARCH time series concept to continuous time, which has been suggested by Klüppelberg, Lindner and Maller [C. Klüppelberg, A. Lindner, R. Maller, A continuous-time GARCH process driven by a Lévy process: Stationarity and second order behaviour, Journal of Applied Probability 41 (2004) 601-622]. We show that any COGARCH process can be represented as the limit in law of a sequence of GARCH(1,1) processes. As a by-product we derive the infinitesimal generator of the bivariate Markov process representation of COGARCH. Moreover, we argue heuristically that COGARCH and the classical bivariate diffusion limit of Nelson [D. Nelson, ARCH models as diffusion approximations, Journal of Econometrics 45 (1990) 7-38] are probably the only continuous-time limits of GARCH.

Keywords: GARCH; Continuous; time; Limit; theorem; Markov; process; Generator (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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