We collect some continuous time GARCH models and report on how they approximate discrete time GARCH processes. Similarly, certain continuous time volatility models are viewed as approximations to discrete time volatility models. 1 Stochastic volatility models and discrete GARCH Both stochastic volatility models and GARCH processes are popular models for the description of financial time series....

The research of Kim and Schmidt (1993) is extended to examine the properties of asymmetric unit root tests in the presence of generalised autoregressive conditional heteroskedasticity (GARCH). Using Monte Carlo simulation, threshold autoregressive and momentum—threshold autoregressive asymmetric unit tests are shown to suffer greater size distortion than the original (implicitly symmetric) Dick...

This paper aims to investigate a Bayesian sampling approach to parameter estimation in the 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 standard deviat...

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, we...

Conditional quantile estimation is an essential ingredient in modern risk management. Although GARCH processes have proven highly successful in modeling financial data it is generally recognized that it would be useful to consider a broader class of processes capable of representing more flexibly both asymmetry and tail behavior of conditional returns distributions. In this paper, we study esti...

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...