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Journal of Applied Mathematics and Decision Sciences
Volume 2006, Article ID 86320, 23 pages

Recent developments in volatility modeling and applications

1Department of Statistics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2
2Department of Supply Chain Management, University of Manitoba, Winnipeg, MB, Canada R3T 2N2
3Department of Business Administration, University of Manitoba, Winnipeg, MB, Canada R3T 2N2

Received 21 February 2006; Revised 10 July 2006; Accepted 24 September 2006

Copyright © 2006 A. Thavaneswaran et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In financial modeling, it has been constantly pointed out that volatility clustering and conditional nonnormality induced leptokurtosis observed in high frequency data. Financial time series data are not adequately modeled by normal distribution, and empirical evidence on the non-normality assumption is well documented in the financial literature (details are illustrated by Engle (1982) and Bollerslev (1986)). An ARMA representation has been used by Thavaneswaran et al., in 2005, to derive the kurtosis of the various class of GARCH models such as power GARCH, non-Gaussian GARCH, nonstationary and random coefficient GARCH. Several empirical studies have shown that mixture distributions are more likely to capture heteroskedasticity observed in high frequency data than normal distribution. In this paper, some results on moment properties are generalized to stationary ARMA process with GARCH errors. Application to volatility forecasts and option pricing are also discussed in some detail.