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On the Normal Inverse Gaussian Distribution in Modeling Volatility in the Financial Markets
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
2002 (Swedish)Doctoral thesis, monograph (Other academic)
Abstract [en]

We discuss the Normal inverse Gaussian (NIG) distribution in modeling volatility in the financial markets. Refining the work of Barndorff-Nielsen (1997) and Andersson (2001), we introduce a new parameterization of the NIG distribution to build the GARCH(p,q)-NIG model. This new parameterization allows the model to be a strong GARCH in the sense of Drost and Nijman (1993). It also allows us to standardized the observed returns to be i.i.d., so that we can use standard inference methods when we evaluate the fit of the model.

We use the realized volatility (RV), calculated from intraday data, to standardize the returns of the ECU/USD foreign exchange rate. We show that normality cannot be rejected for the RV-standardized returns, i.e., the Mixture-of-Distributions Hypothesis (MDH) of Clark (1973) holds. {We build a link between the conditional RV and the conditional variance. This link allows us to use the conditional RV as a proxy for the conditional variance. We give an empirical justification of the GARCH-NIG model using this approximation.

In addition, we introduce a new General GARCH(p,q)-NIG model. This model has as special cases the Threshold-GARCH(p,q)-NIG model to model the leverage effect, the Absolute Value GARCH(p,q)-NIG model, to model conditional standard deviation, and the Threshold Absolute Value GARCH(p,q)-NIG model to model asymmetry in the conditional standard deviation. The properties of the maximum likelihood estimates of the parameters of the models are investigated in a simulation study.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2002. , 169 p.
Studia Statistica Upsaliensia, ISSN 1104-1560 ; 5
Keyword [en]
Informatics, computer and systems science, Volatility modeling, inverse Gaussian, normal inverse Gaussian, realized volatility, GARCH
Keyword [sv]
Informatik, data- och systemvetenskap
National Category
Computer and Information Science
Research subject
URN: urn:nbn:se:uu:diva-2000ISBN: 91-554-5298-1OAI: oai:DiVA.org:uu-2000DiVA: diva2:161613
Public defence
2002-05-17, Hörsal 2, Ekonomikum, Uppsala, 10:15
Available from: 2002-04-25 Created: 2002-04-25Bibliographically approved

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