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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Kallsen, Jan¹  Vesenmayer, Bernhard² 

[1] Univ Kiel, Math Seminar, D-24098 Kiel, Germany

[2] Tech Univ Munich, Zentrum Math, HVB Stiftungsinst Finanzmath, D-85747 Garching, Germany

关键词: GARCH;    Continuous time;    Limit theorem;    Markov process;    Generator;   

DOI  :  10.1016/j.spa.2007.12.008

来源: Elsevier

【 摘 要 】

COGARCH is an extension of the GARCH time series concept to continuous time, which has been suggested by Kluppelberg, Lindner and Maller [C. Kluppelberg, A. Lindner, R. Maller, A continuous-time GARCH process driven by a Levy 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. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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