歐債危機期間歐元兌美元匯率之不對稱GARCH市場風險值研究

Abstract

本研究以對稱的GARCH模型，及兩種不對稱的GARCH模型(旋轉效果的GJR-GARCH模型，及平移效果的NA -GARCH模型)為架構，並引進四種不同的報酬結構，分別估計歐元兌美元匯率報酬率之VaR，探討不同的GARCH模型及報酬結構組合中，何種模型對於歐債危機期間歐元兌美元匯率報酬率之預測能力及風險管理能力最佳。 本研究之主要發現如下： (1)不對稱GARCH模型不一定絕對優於對稱GARCH模型。 (2)NA-GARCH模型的穿透次數平均而言較少，若加進其他指標進行全面分析， 在NA-GARCH模型中，以ARMA-NA-GARCH模型估計歐元兌美元匯率VaR之表現最佳，亦為歐元兌美元匯率最適合且最有效的風險管理模型。 (3)大致而言，穿透次數愈少的模型，其資本準備提列亦愈高，此反映了資本效率與保守性之兩難。 (4)相較於GJR-GARCH模型，NA-GARCH模型所致之不對稱效果相對較小，此較小的不對稱效果應用於資料型態相對穩定的匯率VaR估計及風險管理成效較好。

In this paper, we use a symmetric GARCH model and two asymmetric GARCH models (innovation-rotated GJR-GARCH and level-shifted NA-GARCH models) with various forms of mean equations to find out the most appropriate model for estimating the VaR of EUR/USD exchange rates during the European debt crisis. We compare the estimated VaR with realized return and evaluate the performance of the GARCH models in managing the market risk of EUR/USD exchange rates based on the indicators such as violation numbers, mean violation, aggregate violation, and maximum violation. In our empirical studies, the major findings are listed below: (1)Asymmetric GARCH models not necessarily outperform symmetric GARCH models all the time. (2)On average, the NA-GARCH models outperform other GARCH models in terms of violation numbers. Among NA-GARCH models with different forms of mean equations, we find that ARMA(1,1)-NA-GARCHM(1,1) is superior than other GARCH models in estimating the VaR of EUD/USD exchange rates in terms of violation numbers, aggregate violation range, and maximum violation range . Therefore, ARMA(1,1)-NA-GARCHM(1,1) is the best-fitting model and the most effective model in risk management of EUD/USD exchange rates. (3)In general, the less occurrence of violation is accompanied with the larger provision of capital reserve. It reflects the tradeoff between capital efficiency and conservativeness. (4)Compared with GJR-GARCH models, the relatively smaller asymmetric effect of NA-GARCH models (ARMA(1,1)-NA-GARCHM(1,1)) fits better with the relatively steady feature of the foreign exchange rates.