Workshop: Advanced Modeling in Finance and Insurance
Time: Mon, September 22, 2008, 10:50-11:40
Speaker: Claudia Klüppelberg
Abstract
The continuous-time GARCH [COGARCH(1,1)] model, driven by a single Lévy noise process, exhibits the same second order properties as the discrete-time GARCH(1,1) model.
Moreover, the COGARCH(1,1) model has heavy tails and clusters in the extremes. The second order structure of the COGARCH(1,1) model allows for some estimation procedure
based on the ARMA(1,1) autocorrelation structure of the model and other moments. The statistical analysis also provides an estimator for the volatility. Furthermore, a sequence of GARCH(1,1) models can be found, which approximates the COGARCH(1,1) model in the Skorokhod metric. The model shows certain similarities, but also differences, to the Lévy-driven Ornstein-Uhlenbeck model. We also discuss some recent developments and extensions
of our model.
References
[1] Fasen, V. (2007) Asymptotic results for sample autocovariance functions and extremes
of integrated generalized Ornstein-Uhlenbeck processes. Preprint. TU München. Submitted.
[2] Haug, S., Klüppelberg, C., Lindner, A., Zapp, M. (2007) Method of moment estimation
in the COGARCH(1,1) model The Econometrics Journal, 10, 320-341.
[3] Klüppelberg, C., Lindner, A., Maller, R. (2004) A continuous time GARCH process
driven by a Lévy process: stationarity and second order behaviour. J. Appl. Prob. 41(3),
601-622.
[4] Maller, R. A., Müller, G. and Szimayer, A. (2007) GARCH modelling in continuous time for irregularly spaced time series data. Bernoulli. To appear.
[5] Müller, G., Durand, R., Maller, R. and Klüppelberg, C. (2009) Analysis of stock market
volatility by continuous-time GARCH models. In: Gregoriou, G.N. (2009) Stock Market
Volatility. Chapman Hall/Taylor and Francis, London. To appear.
Presentation slides (pdf, 1.1 MB)
URL: www.ricam.oeaw.ac.at/specsem/sef/events/program/presentation.php
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