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An Exponential Continuous-Time GARCH Process

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Stephan Haug  and
Claudia Czado
Stephan Haug*
Affiliation:
Munich University of Technology
Claudia Czado*
Affiliation:
Munich University of Technology
*
∗Postal address: Center for Mathematical Sciences, Munich University of Technology, D-85747 Garching, Germany.
∗Postal address: Center for Mathematical Sciences, Munich University of Technology, D-85747 Garching, Germany.
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Abstract

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In this paper we introduce an exponential continuous-time GARCH(p, q) process. It is defined in such a way that it is a continuous-time extension of the discrete-time EGARCH(p, q) process. We investigate stationarity, mixing, and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous-time GARCH(p, p) model.

Keywords

Exponential continuous-time GARCH processEGARCHLévy processstationarityleverage effectstochastic volatility

MSC classification

Secondary: 60G10: Stationary processes 60G12: General second-order processes 91B70: Stochastic models 91B84: Economic time series analysis
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 960 - 976
Copyright
Copyright © Applied Probability Trust 2007 

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