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Asymmetric COGARCH processes

Part of: Inference from stochastic processes Parametric inference Stochastic processes

Published online by Cambridge University Press:  30 March 2016

Anita Behme ,
Claudia Klüppelberg  and
Kathrin Mayr
Anita Behme
Affiliation:
Center for Mathematical Sciences, Technische Universität München, 85748 Garching, Boltzmannstrasse 3, Germany. Email address: behme@ma.tum.de.
Claudia Klüppelberg
Affiliation:
Center for Mathematical Sciences, Technische Universität München, 85748 Garching, Boltzmannstrasse 3, Germany. Email address: cklu@ma.tum.de.
Kathrin Mayr
Affiliation:
Center for Mathematical Sciences, Technische Universität München, 85748 Garching, Boltzmannstrasse 3, Germany.
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Abstract

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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.

Keywords

APCOGARCHasymmetric power COGARCHCOGARCHfirst-jump approximationcontinuous-time GARCHGJR-GARCHGJR-COGARCHmaximum-likelihood estimationhigh-frequency datamethod of momentsstochastic volatility

MSC classification

Primary: 60G10: Stationary processes 60G51: Processes with independent increments; L'evy processes 62M05: Markov processes
Secondary: 62F10: Point estimation 62M10: Time series, auto-correlation, regression, etc.
Type
Part 5. Finance and econometrics
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 161 - 173
Copyright
Copyright © Applied Probability Trust 2014 

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