We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the Metropolis-Hastings algorithm and the parameters of the proposal density are determined adaptively by using the data sampled by the Markov chain Monte Carlo simulation...

This paper investigates the forecasting ability of four different GARCH models and the Kalman filter method. The four GARCH models applied are the bivariate GARCH, BEKK GARCH, GARCH-GJR and the GARCH-X model. The paper also compares the forecasting ability of the non-GARCH model the Kalman method. Forecast errors based on twenty UK company weekly stock return (based on timevary beta) forecasts ...

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 Duan, Gauthier and Simonato (1999), an analytical approximate formula for European options in the GARCH framework was developed. The formula is however restricted to the nonlinear asymmetric GARCH model. This paper extends the same approach to two other important GARCH specifications GJR-GARCH and EGARCH. We provide the corresponding formulas and study their numerical performance. keywords: ...

The three most popular univariate conditional volatility models are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). The underlying stochastic specification to obtain GARCH was demonstr...

This research estimates portfolio VaR (Value-at-Risk) on G7 exchange rates using a GJR-GARCH-EVT (extreme value theory)-Copula based approach. We first extracts the filtered residuals from each return series via an asymmetric GJR-GARCH model, then constructs the semi-parametric empirical marginal cumulative distribution function (CDF) of each asset using a Gaussian kernel estimate for the inter...

The present study aims at applying different methods i.e GARCH, EGARCH, GJRGARCH, IGARCH & ANN models for calculating the volatilities of Indian stock markets. Fourteen years of data of BSE Sensex & NSE Nifty are used to calculate the volatilities. The performance of data exhibits that, there is no difference in the volatilities of Sensex, & Nifty estimated under the GARCH, EGARCH, GJR GARCH, I...

We propose a method of estimating the Pareto tail thickness parameter of the unconditional distribution of a financial time series by exploiting the implications of a GJR-GARCH volatility model. The method is based on some recent work on the extremes of GARCH-type processes. We show that the estimator of tail thickness is consistent and converges at rate √ T to a normal distribution (where T is...

This paper examines the forecasting performance of four GARCH(1,1) models (GARCH, EGARCH, GJR and APARCH) used with three distributions (Normal, Student-t and Skewed Student-t). We explore and compare different possible sources of forecasts improvements: asymmetry in the conditional variance, fat-tailed distributions and skewed distributions. Two major European stock indices (FTSE 100 and DAX 3...