Müller, G., Durand, R., Maller, R., Klüppelberg, C.
Analysis of stock market volatility by continuous-time GARCH models
The discrete time ARCH/GARCH model of Engle and Bollarslev has been enormously
influential and successful in the modelling of financial data. Recently, Kl¨uppelberg,
Lindner, and Maller (2004) introduced the so-called “COGARCH” model as a continuoustime
analogue to the GARCH model. Many aspects of the COGARCH have been investigated,
including various of its theoretical properties, its relations to other continuous-time
models, and the estimation of the parameters in it. We review some of these results in the
present paper, and go on to apply the COGARCH to 5-minute data on the S&P500 index,
in order to illustrate its ability to analyse stochastic volatility in very high-frequency,
irregularly spaced, financial data.