Various e m p i r i d studies have shown that the time-varying volatility of asset returns can be described by GARCH (generalized autoregressive conditional heteroskedasticity) models. The corresponding GARCH option pricing model of Duan (1995) is capable of depicting the "smile-effect" which often can be found in option prices. In some derivative markets, however, the slope of the smile is not...

This paper aims to investigate a Bayesian sampling approach to parameter estimation in the semiparametric GARCH model with an unknown conditional error density, which we approximate by a mixture of Gaussian densities centered at individual errors and scaled by a common standard deviation. This mixture density has the form of a kernel density estimator of the errors with its bandwidth being the ...

Economic and financial time series typically exhibit time varying conditional (given the past) standard deviations and correlations. The conditional standard deviation is also called the volatility. Higher volatilities increase the risk of assets, and higher conditional correlations cause an increased risk in portfolios. Therefore, models of time varying volatilities and correlations are essent...

This paper studies volatility forecasting in the financial stock market. In general, stock market volatility is time-varying and exhibits clustering properties. Thus, this paper presents the results of using a fuzzy system method to analyze clustering in generalized autoregressive conditional heteroskedasticity (GARCH) models. It also uses the adaptive method of recursive least-squares (RLS) to...