Journal of Applied Probability

Asymmetric COGARCH processes

Anita Behme, Claudia Klüppelberg, and Kathrin Mayr


Financial data are as a rule asymmetric, although most econometric models are symmetric. This applies also to continuous-time models for high-frequency and irregularly spaced data. We discuss some asymmetric versions of the continuous-time GARCH model, concentrating then on the GJR-COGARCH model. We calculate higher-order moments and extend the first-jump approximation. These results are prerequisites for moment estimation and pseudo maximum likelihood estimation of the GJR-COGARCH model parameters, respectively, which we derive in detail.

Article information

J. Appl. Probab., Volume 51A (2014), 161-173.

First available in Project Euclid: 2 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G10: Stationary processes 60G51: Processes with independent increments; Lévy processes 62M05: Markov processes: estimation
Secondary: 62F10: Point estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 90G70

APCOGARCH asymmetric power COGARCH COGARCH first-jump approximation continuous-time GARCH GJR-GARCH GJR-COGARCH maximum-likelihood estimation high-frequency data method of moments stochastic volatility


Behme, Anita; Klüppelberg, Claudia; Mayr, Kathrin. Asymmetric COGARCH processes. J. Appl. Probab. 51A (2014), 161--173. doi:10.1239/jap/1417528473.

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