Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 86320, 23 pages
doi:10.1155/JAMDS/2006/86320
Recent developments in volatility modeling and applications
1Department of Statistics, University of Manitoba, Winnipeg R3T 2N2, MB, Canada
2Department of Supply Chain Management, University of Manitoba, Winnipeg R3T 2N2, MB, Canada
3Department of Business Administration, University of Manitoba, Winnipeg R3T 2N2, MB, Canada
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.
Abstract
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 byThavaneswaran
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.