Modeling Daily Return Volatility Through GJR(1,1) Model and Realized Volatility Measure
Keywords:
ARWM, GJR model, Excel’s Solver’s GRG non-linear, realized kernel, student-t distributionAbstract
The Glosten–Jagannathan–Runkle (GJR) model is an extension of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model by adding an asymmetric term to allow conditional volatility to respond differently to the past returns based on their signs. Given the high-frequency data, the Realized Volatility (RV) measures have received great attention. This study investigates the fitting performance of the conventional GJR(1,1) model and two extended GJR models incorporating the Realized Kernel as an RV component, namely the GJR-X(1,1) and RealGJR(1,1), with two different return error distributions, namely Normal and Student-t, on the Financial Times Stock Exchange 100 (FTSE100) index for the daily period from January 2000 to December 2017. The study begins by
evaluating the estimation ability of the Excel’s Solver’s GRG Non-Linear method, which is a simple and easy tool for financial practitioner, and the ARWM (Adaptive Random Walk Metropolis) method requiring computer programming knowledge. This study found that the Excel’s Solver’s GRG NonLinear method is an easy and accurate estimation tool as the estimated values are relatively close to the ARWM results. To select the best fit model amongst competing models, the Akaike Information Criterion (AIC) statistical method was used. On the basis of AIC, this study found the empirical merit of the RealGJR(1,1) model with Student-t distribution, that is its potential to provide the best fit model at any sample sizes. The class of RealGJR(1,1) model exhibits lowest risk than the others so
that investors intend to keep the stocks and is most capable of capturing rapid changes in the volatility level. These results are highly recommended to the financial practitioners and analysts dealing with high frequency financial data and GJR volatility modeling.
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