Recent developments in volatility modeling and applications

摘要

In financial modeling, it has been constantly pointed out thatvolatility clustering and conditional nonnormality induced leptokurtosis observedin high frequency data. Financial time series data are not adequatelymodeled by normal distribution, and empirical evidence on the non-normalityassumption is well documented in the financial literature (details are illustrated by Engle (1982) and Bollerslev (1986)). An ARMA representation has been used byThavaneswaranet al., in 2005, to derive the kurtosis of the various class of GARCHmodels such as power GARCH, non-Gaussian GARCH, nonstationary andrandom coefficient GARCH. Several empirical studies have shown that mixturedistributions are more likely to capture heteroskedasticity observed in high frequencydata than normal distribution. In this paper, some results on momentproperties are generalized to stationary ARMA process with GARCH errors.Application to volatility forecasts and option pricing are also discussed in somedetail.