GJR-GARCH model in value-at-risk of financial holdings

Abstract

In this study, we introduce an asymmetric Generalized Autoregressive Conditional Heteroscedastic (GARCH) model, Glosten, Jagannathan and Runkle-GARCH (GJR-GARCH), in Value-at-Risk (VaR) to examine whether or not GJR-GARCH is a good method to evaluate the market risk of financial holdings. Because of lacking the actual daily Profit and Loss (P&L) data, portfolios A and B, representing FuBon and Cathay financial holdings are simulated. We take 400 observations as sample group to do the backward test and use the rest of the observations to forecast the change of VaR. We find GJR-GARCH works very well in VaR forecasting. Nonetheless, it also performs very well under the symmetric GARCH-in-Mean (GARCH-M) model, suggesting no leverage effect exists. Further, a 5-day moving window is opened to update parameter estimates. Comparing the results under different models, we find that the model is more accurate by updating parameter estimates. It is a trade-off between violations and capital charges.