Determination of Risk Value Using the ARMA-GJR-GARCH Model on BCA Stocks and BNI Stocks

Abstract

Stocks are common investments that are in great demand by investors. Stocks are also an investment instrument that provides returns but tends to be riskier. The return time series is easier to handle than the price time series. In investment activities, there are the most important components, namely volatility and risk. All financial evaluations require accurate volatility predictions. Volatility is identical to the conditional standard deviation of stock price returns. The most frequently used risk calculation is Value-at-Risk (VaR). Mathematical models can be used to predict future stock prices, the model that will be used is the Glosten Jagannathan Runkle-generalized autoregressive conditional heteroscedastic (GJR-GARCH) model. The purpose of this study was to determine the value of the risk obtained by using the time series model. GJR-GARCH is a development of GARCH by including the leverage effect. The effect of leverage is related to the concept of asymmetry. Asymmetry generally arises because of the difference between price changes and value volatility. The method used in this study is a literature and experimental study through secondary data simulations in the form of daily data from BCA shares and BNI shares. Data processing by looking at the heteroscedasticity of the data, then continued by using the GARCH model and seeing whether there is an asymmetry in the data. If there is an asymmetric effect on the processed data, then it is continued by using the GJR-GARCH model. The results obtained on the two stocks can be explained that the analyzed stock has a stock return volatility value for the leverage effect because the GJR-GARCH coefficient value is > 0. So, the risk value obtained by using VaR measurements on BCA stocks is 0.047247 and on BNI stocks. is 0.037355. Therefore, the ARMA-GJR-GARCH model is good for determining the value of stock risk using VaR.