NA-GARCH模型於金融控股公司市場風險值之研究

Abstract

本研究檢驗兩種不對稱GARCH模型，旋轉效果的EGARCH 模型和平移效果的NA-GARCH 模型在VaR 預測值上的表現。報酬結構上亦有ARMA(1,1) ,AR(1), MA(1) ,即“in –mean”模型的變化。我們分別模擬A 、B兩個資產組合代表台灣的兩家金控公司，針對216個樣本點，在99 % 和95 % 的信心水準下，VaR 預測值的檢測以損失的超出次數為基準，配合其他指標如VaR 平均值，平均損失、累積損失、最大損失以期達到模型的有效性及資本提列的效率性。本研究的主要發現如下 ： 1.所有的VaR 預測模型都小於預定的超出次數，除ARMA(1,1) 在 99% 信心水準下以外，因此可視為合格的內部VaR市場風險模型。 2.ARMA(1,1) 模型雖然和真實的P & L有相似的波動趨勢，但遞延一期的效果卻造成更大的損失超出次數；此外，過大的波動幅度疑為過度配置下的結果。 3.在既定的模擬組合和觀測時間下，無法產生單一最佳的VaR預測模型，亦無法辨別是為旋轉或平移的不對稱效果主導市場的報酬波動變化。

In this paper, we employ EGARCH ,representing rotation asymmetry effect, and NA-GARCH, representing shift asymmetry effect, with variations in their mean equations : ARMA(1,1) ,AR(1), MA(1) ,and “ in –mean” models as VaR forecast models. Forward testing of one day-ahead VaR performance under 99 % and 95 % confidence levels is evaluated with realized P &L for 216 observations in two simulated portfolios standing for financial holdings in Taiwan. Based on violation number, we also consider other performance indicators such as mean VaR, aggregate, mean and max violation to strike a balance between model effectiveness and capital charge efficiency. The main findings are as follows： 1.All the VaR forecast models, except for ARMA(1,1) under 99%, in EGARCH and NA-GARCH achieve the targeted violation rate and can be viewed as qualified internal models for banks. 2.ARMA(1,1) models have almost the same volatile trend as real P& L time series, yet the one day lag makes more violations. In addition, the excessive volatility is the implication of overfitting problem. 3.No particular VaR model can distinctively outperform others and serves as the best-fitting model, nor can we tell the shift or the rotation asymmetric effect dominates the portfolios during the observation period.