DIA之不對稱GARCH市場風險值之研究

Abstract

本研究採用兩種不對稱 GARCH 模型 -分別為代表旋轉效果的 GJR-GARCH 模型以及代表平移效果的 NA-GARCH 模型- 以之與對稱的GARCH 模型相比較，以期探討何種 GARCH 模型對於 VaR 的預測有較佳的表現。 另外為探討不同報酬結構對於 VaR 的預測是否會產生影響，本研究將四種報酬結構導入前述三種 GARCH 模型，分別為 ARMA(1,1)，AR(1)，MA(1)與「in-mean」。 本研究所採用的測試樣本為自西元 2000 年 12 月 31 日起至 2006年 12 月 29 號止之每日報酬為樣本點，再取其中的 860 個樣本點以估計參數，餘下之 400 的樣本點則用以在 99％與 95％的信賴水準下比較各 GARCH 模型所估計出的市場風險值，並比較其預測能力。 本研究的主要發現如下： 1. 本研究發現當應用於 DIA 時，代表不對稱 GARCH 模型的 GJR-GARCH與 NA-GARCH 在衡量市場風險時均有優異表現，而對稱的 GARCH 模型表現則較不佳。在 99％信賴水準下，MA(1)-GARCHM(1,1)的違反個數為 14 個，是唯一超出 Basel Non-Rejection Range 的模型。 此外，兩種不對稱模型中以代表旋轉效果的GJR-GARCH表現最好。 2. 本研究所採用的四種報酬結構當應用於代表旋轉效果的 GJR-GARCH 和平移效果的 NA-GARCH 不對稱模型時，所產生的違反個數所差無幾，可知不同的報酬結構對預測 VaR 的正確性並未產生重大影響，而含有更多參數的模型對 VaR 預測的能力也並未有明顯的優勢。同時在 ARMA(1,1)下的違反個數並沒有明顯比其他報酬結構多出許多，故看不出有明顯的過度配置現象。

In this study we adopt two asymmetric GARCH models, with GJR-GARCH represent the rotation asymmetric effect; and NA-GARCH for the shift asymmetric effect, to compare their performance on VaR forecasting to the symmetric GARCH model. With variance of their mean equations which are ARMA(1,1), AR(1), MA(1), and “in-mean”. We introduce the close price of DIA and use its daily return as sample, stretching from Dec. 31, 2000 to Dec. 29, 2006. We use 860 observations for parameters estimates; the rest 400 will be used by different models to forecast VaR in 99% and 95% confidence level then been evaluated. The major findings in this study are: 1. The asymmetric GJR-GARCH and NA-GARCH models have fairly well performance on VaR forecasting, while symmetric GARCH model has the poorest performance. In 99% confidence level, MA(1)-GARCHM(1,1) generate fourteen violations and is the one model to exceed Basel Non-Rejection Range. This thesis conclude that in forecasting VaR of DIA, asymmetric GARCH models have superior performance than that of the symmetric one, and the GJR-GARCH with rotation effect has the most outstanding outcome. 2. In asymmetric GARCH models, GJR families that represent rotation asymmetric and NA families that represent shift, we can’t find solid proof of whether introducing new information would always improve the forecast accuracy of a model, for the four mean equations generate almost identical violation rate under the same asymmetric GARCH model. In the mean time, we can’t find significant improvement of VaR forecasting ability of the model with more parameters. Also the ARMA(1,1) mean equation doesn’t generate obvious more violations than other models do, so we can’t determine any clearly over-fitting situation.