QQQQ之不對稱GARCH市場風險值之研究

Abstract

市場風險值VaR是近年來在國際間被廣泛應用的一種風險管理工具，本篇論文主要採用了兩種不同效果的不對稱GARCH模型，分別為具有旋轉效果的GJR-GARCH模型與具有平移效果的NA-GARCH模型，將期預測的結果與對稱的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。此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」。 資料我們採用的是代表NASDAQ-100指數的ETF QQQQ，資料觀察期間為2002年1月14日到2009年2月27日之每日報酬共1800筆樣本點.我們使用前1200筆樣本來做配適模型與模型的參數估計，使用後600筆樣本點則用以在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。 本研究的主要成果如下： (1) 不對稱的GARCH模型並非總是優於對稱GARCH模型，本篇的對稱GARCH模型預測結果優於不對稱的NA-GARCH模型。 (2) 實證結果發現GJR-GARCH 模型不論是在95%或是99%信心水準下都有較佳的預測能力。在四種不同報酬結構的GJR-GARCH 模型中又以ARMA(1,1)-GJR-GARCHM(1,1)表現最佳。 (3) 以過去資料配適建構的GARCH模型無法非常準確的預測次級貸款金融風暴期間時的報酬波動，然而可採用較近期的資料配適模型來解決此一問題。

VaR is a newly developed tool for risk management that had been used international wide. In this paper 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 with VaR forecasting of the symmetric GARCH model. In addition, we employ different mean equations which are ARMA(1,1), AR(1), MA(1), and “in-mean” in order to find out a more appropriate GARCH method in estimating VaR of QQQQ. We pick up the latest 1800 daily information of QQQQ from 2002/01/14 to 2009/02/27. We use 1200 observations for parameters estimates; the rest 600 will be used by different models to forecast VaR in 99% and 95% confidence level then been evaluated. Our major findings contain several aspects as follows: (1) Asymmetric GARCH models do not always outperform symmetric GARCH models (GARCHM model). (2) The empirical results show that GJR-GARCH models have better performance in estimating VaR through the forward test analysis under 95% and 99% confidence level. Among GJR-GARCH models with four types of mean equations, we distinctly find out ARMA(1,1)-GJR- GARCHM(1,1) is the best fitted model. (4) The GARCH models which are estimated by past data cannot forecast the VaR precisely during subprime crisis. However, this problem can be solved by adopting update models which are estimated by recent data.