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.

A parsimonious parametric model for generating margin requirements for futures

“…17 GJR-GARCH models are given by σ2 t,T = β0 + β1r and Nelson (1990)'s exponential GARCH model is ln σt,T = β0 + g(rt−1,T ) + β3 ln σt−1,T , where g(rt−1,T ) = β1rt−1,T + β2(|rt−1,T | − E[|rt,T |]). For instance Su et al (2011) argue that GJR-GARCH is best for forecasting one-day-ahead downside risk and Chen et al (2012), propose the use of Laplace innovations with GJR-GARCH. Non-parametric VaR methods interpolate the quantile from an empirical distribution of historical returns and these methods are reviewed and compared in Alexander (2008).…”

Borsa İstanbul-100 Endeksi̇ni̇n Yi̇yecek-İçecek Sektörü Endeksi̇ Ve Teknoloji̇ Sektörü Endeksi̇ Karşisindaki̇ Volati̇li̇tesi̇

“…The GJR-GARCH model is introduced in VaR to analyze whether it is a superior method to review the market risk of financial assets or not (Su, Huang & Lin, 2011). …”

Determination of Value-at-Risk in UNVR Stocks Using ARIMA-GJR-GA RCH Model

“…Based on the analysis of the paper, the ARIMA model (1,1,1)-GJR-GARCH (1,1) is the best model for exchange rates and forecasting. Su & Lin (2011) determines Value-at-Risk using the GJR-GARCH model against financial ownership. The result obtained is that Model GJR-GARCH is good for VaR forecasting.…”

“…There are some flaws in the models that have been carried out by some previous researchers. Among others Xu et al (2015) have not linked their research to the determination of VaR values, Su & Lin (2011) have not determined the value of risk using Conditional Value-at-Risk (CVaR).…”