GARCH模型對匯率風險值之估計

Using GARCH Models to Estimate Value at Risk of Exchange Rates

劉錫山(Hsi-Shan Liu)

指導教授 ： 林建甫

國立臺灣大學/社會科學院/經濟學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.00045

摘要

近期的財務金融文獻，普遍同意波動性變化具有因時而異且有叢聚的特性，包括Morgan (1976)、Engle (1982)、Bollerslev (1986)、Engle and Manganelli (2000)…等，因此本研究採用最能描繪自我相關條件異質變異的GARCH族模型進行匯率報酬率之風險值估計。至於樣本大小之選擇，因本研究是利用滾動程序(rolling)方法來估計風險值，故使用三種不同的視窗長度1年、3年和5年來預測同一組樣本外觀察值，藉以觀察不同的視窗長度對於風險值模型的績效結果影響。
Pritsker (1997)認為在風險管理實務上，風險值應兼具準確性及即時性，但往往兩者會呈一抵換關係。本研究於績效評估上，是依據Engel and Gizycki (1999)所提出三個評估準則—準確性、保守性及效率性，以藉由不同的角度衡量各風險值模型之優缺。以往大部分文獻皆直接比較評估模型何者較具準確性、保守性或效率性，而本文較為不同的是鎖定同一視窗長度，比較各模型的績效，或鎖定同一模型，比較視窗長度對風險值模型的績效影響，以期望使用交叉方式能發現較明確的結果。
本研究利用滾動程序(rolling)方法來預測風險值，結果發現以1年的視窗長度，並無法讓其移動視窗所估計出之係數皆符合參數約束條件，而使計算出的風險值失去有效性，且在相同的風險值模型之保守性或效率性方面，易受到視窗長度的影響。另外，本研究亦發現使用GARCH模型估計風險值時，在均數方程式引入「風險貼水」項，或變異數方程式採用自然對數形式，皆無法改進風險值模型之績效。

關鍵字

自我相關條件異質變異 ； GARCH ； 滾動程序 ； 風險值 ； 視窗長度

並列摘要

Recent financial/risk management papers indicates that the finance market liquidity is time variant and tends to be cluster (Morgan (1976)、Engle (1982)、Bollerslev (1986)、Engle and Manganelli (2000)). Thus this research use GARCH model as VaR model since GARCH model is best to describe autoregressive conditional heteroscedasticity. We used rolling process to evaluate the value of risk and we selected the window size of 1 year, 3 years, and 5 years for the same samples to estimate the observation value out side the window. Through the estimate, we can evaluate the effect on the VaR model from different window size.
When risk management applied in practice, value at risk (VaR) should reflect the risk precisely and promptly. However, often real time results can hardly precise (Pritsker 1997). Based on the guide line from Engel and Gizycki (1999), accuracy, stability, and performance, we present this paper a different view of evaluating the pro and con of varies VaR model. In the past, most of the reports compare Value at Risk model directly in term of accuracy, stability, and performance. This paper presents a different approach by fixing the window size to compare the performance or by fixing the model to compare the valuation of different window size. From the above approach, we expect to obtain a much detail comparison.
In this paper, we use rolling process to estimate Value at Risk. Our results show that using one year window, we can't let all the estimates from the rolling window converge to their restrictions, therefore the estimates become invalid. At the same time, our results also show that under the same model, stability and the performance are both very sensitive to window size as well. We also found neither by adding risk premium to the mean equation, nor by using LOG-GARCH can improve the valuation of the VaR model.

並列關鍵字

Autoregressive Conditional Heteroscedasticity ； GARCH ； Rolling Process ； Value at Risk ； Rolling Window Size

參考文獻

林楚雄等(2006)，「三種修正歷史模擬法估計風險值模型之比較」，《風險管理學報》，第七卷第二期，頁183-201。

周雨田等(2004)，「動態波動模型預測能力之比較與實證」，《財金論文叢刊》，2004年6月第一期，頁1-23。

張簡彰程等(2008)，「風險矩陣波動修正之風險值估計」，《輔仁管理評論》，第15卷第2期，頁61-82。

Alexander, C. O. & C. T. Leigh (1997), On the Covariance Matrices Used in Value at Risk Models. Journal of Derivatives 4(3) : 50-62.

Bollerslev, T. (1986), “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, 31, 307-327.