The autoregressive conditional heteroskedasticity (ARCH) and generalized autoregressive conditional heteroskedasticity (GARCH) models take the dependency of the conditional second moments. The idea behind ARCH/GARCH model is quite intuitive. For ARCH models, past squared innovations describes the present squared volatility. For GARCH models, both squared innovations and the past squared volatil...

Nowadays many researchers use GARCH models to generate volatility forecasts. However, it is well known that volatility persistence, as indicated by the sum of the two parameters G1 and A1[1], in GARCH models is usually too high. Since volatility forecasts in GARCH models are based on these two parameters, this may lead to poor volatility forecasts. It has long been argued that this high persist...

Since ARCH and GARCH models are presented, more and more authors are interested in the study of volatilities in financial markets with GARCH models. Method for estimating the coefficients of GARCH models is mainly the maximum likelihood estimation. Now we consider another method—MCMC method to substitute for maximum likelihood estimation method. Then we compare three GARCH models based on it. M...

This paper used different copula-based GARCH models (Copula-GARCH model and Copula-GJR-GARCH model) to analyze the dependence structure among gold price, stock price index of gold mining companies and Shanghai Composite Index in China. The empirical results found that the suitable margins were skew-t distribution, and the GJR-GARCH marginal distribution had better explanatory ability than the G...

In the light of regime switching and volatility clustering in the dynamics of SHIBOR, regime-switching CIR model (RSCIR) and regime-switching GARCH CIR model (RSCIR-GARCH) are established by introducing regime-switching and GARCH specifications into CIR model successively. Then, a contrast study among CIR, RSCIR and RSCIR-GARCH models is performed based on SHIBOR sample data, which indicates th...

This paper investigates the hedging effectiveness of time-varying hedge ratios in the agricultural commodities futures markets based on four different versions of the GARCH models. The GARCH models applied are the standard bivariate GARCH, the bivariate BEKK GARCH, the bivariate GARCH-X and the bivariate BEKK GARCH-X. The GARCH-X and the BEKK GARCH-X models are uniquely different from the other...

Extreme value theory is widely used financial applications such as risk analysis, forecasting and pricing models. One of the major difficulties in the applications to finance and economics is that the assumption of independence of time series observations is generally not satisfied, so that the dependent extremes may not necessarily be in the domain of attraction of the classical generalised ex...

In this paper, we introduce a two−dimensional Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model for clutter modeling and anomaly detection. The one−dimensional GARCH model is widely used for modeling financial time series. Extending the one−dimensional GARCH model into two dimensions yields a novel clutter model which is capable of taking into account important characteris...

As extensions to the Black-Scholes model with constant volatility, option pricing models with time-varying volatility have been suggested within the framework of generalized autoregressive conditional heteroskedasticity (GARCH). However, application of the GARCH option pricing model has been hampered by the lack of simulation techniques able to incorporate early exercise features. In the presen...

Many researchers use GARCH models to generate volatility forecasts. We show, however, that such forecasts are too variable. To correct for this, we extend the GARCH model by distinguishing two regimes with different volatility levels. GARCH effects are allowed within each regime, so that our model generalizes existing regime-switching models that allow for ARCH terms only. The empirical applica...