本研究欲以一臺灣投資人身分，在面對匯率及股市的雙重風險下，如何有效衡量風險值，有鑑於金融資產的報酬多具有異質變異性(heteroscedasticity)及波動叢聚(volatility clustering)的現象，且跨市場跨商品之間可能存有相關性，故除了基本的單變量(univariate) GARCH (Generalized Autoregressive Conditional Heteroscedastic)模型及IGARCH (Integrated GARCH)模型外，也考量可捕捉變數之間的固定相關係數－多變量(multivariate) CCC-GARCH (Constant Conditional Correlation GARCH)模型，最後採用穿透率做為精確度的衡量指標。
研究變數採用臺幣對人民幣匯率以及華夏上證50，實證結果顯示，在八年的樣本內資料中，可以捕捉變數之間的固定相關係數CCC-GARCH模型能得到較符合信賴水準的穿透率，表示若已知資產之間存在關聯性，應該採用更複雜的模型，以得到更精確的風險值；IGARCH在基金報酬率上所得到的穿透率比匯率報酬精確，顯示該基金變數具有波動持久性的特徵；此外，在分配假設中，t分配能得到較符合信賴水準的穿透率，表在金融資產報酬率因極端值較多並非呈現傳統假設的常態分配，能夠透過有厚尾(fat-tail)現象的t分配表示真實情況。因此，本研究建議當在估計雙資產的風險值時，可透過t分配假設下CCC-GARCH模型，以獲得最精確的風險值估計值。

This thesis studies the effective measurement of Value-at-Risk (VaR) when investors hold positions involving duel risks from exchange rate market and foreign stock market. GARCH family models are used to incorporate the conditional heteroskedasticity of each individual asset. To further incorporate the correlation between assets, we apply the CCC-GARCH model to improve the performance of VaR estimation. The accuracy of VaR estimation is examined by penetration rates.
The empirical results show that the CCC-GARCH model outperforms other competing models. In the measure of correlation between two assets, models considering correlation across assets are better suited for the estimation of VaR. In addition, the performance of ETF is superior to exchange rate in IGARCH model, showing the phenomenon of volatility persistence. Furthermore, t distribution provides a better estimation than normal distribution revealing the return distribution exhibits tail-fatness. Because of the occurrence of the extreme value, t distribution with the character of fat-tail can reflect the practical situation of financial markets for VaR estimation.

1.林楚雄、邱瓊儀、高子荃「結合GARCH 模型與極值理論的風險值模型」，管理學報，22卷1期，2005年，133−154頁。
2.李沃牆、柯中偉，「外匯投資組合之風險值評估－分量迴歸的應用」，中原企管評論 9卷1期，2011年4月，97−116頁。
3.涂惠娟、蔡垂君，「臺指選擇權風險值之研究」，文大商管學報，11卷2期，2006年，57−69頁。
4.蘇榮斌、黃孟祥，「風險值之預測：以臺灣、韓國、新加坡及馬來西亞等國家股票市場為例」，中華技術學院學報 39期，2008年12月，181−198頁
5.蘇榮斌，「美國股票市場風險值之估計」，中華科技大學學報 48期，2011年7月，179−199頁。
6.Beder, T.S., 1995. VAR: Seductive but Dangerous. Financial Analysts Journal, 51(5), pp.12-24.
7.Bera, A.K. and J. S. Roh, 1991. “A Moment Test of the Consistency of the Correlation in the Bivarite GARCH Model,” Mimeo, Department of Economics, University of Illinois at Urbana-Champaign.
8.Bollerslev, T., 1986. Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), pp.307-327.
9.Bollerslev, T., 1987. A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return. The Review of Economics and Statistics, pp.542-547.
10.Bollerslev, T., 1990. Modelling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized ARCH Model. The Review of Economics and Statistics, pp.498-505.
11.Bollerslev T, Chou RY, Kroner KF. ARCH Mmodeling in Finance: A Review of the Theory and Empirical Evidence. Journal of Econometrics. 1992 Apr 1;52(1-2):5-9.
12.Cassuto, A.E., 1995. Non-Normal Error Patterns: How to Handle Them. The Journal of Business Forecasting, 14(2), p.15.
13.Chou, R.Y.T., 2005. Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model. Journal of Money, Credit, and Banking, 37(3), pp.561-582.
14.Danielsson, J. and de Vries, C.G., 1997. Tail Index and Quantile Estimation with Very High Frequency Data. Journal of Empirical Finance, 4(2-3), pp.241-257.
15.Dickey, D.A. and Fuller, W.A., 1981. Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica: Journal of the Econometric Society, pp.1057-1072.
16.Engle, R.F., 1982. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Unflation. Econometrica: Journal of the Econometric Society, pp.987-1007.
17.Engle, R.F. and Bollerslev, T., 1986. Modelling the Persistence of Conditional Variances. Econometric Reviews, 5(1), pp.1-50.
18. Engle, R., 2002. Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models. Journal of Business & Economic Statistics, 20(3), pp.339-350.
19.Giot, P. and Laurent, S., 2003. Market Risk in Commodity Markets: A VaR Approach. Energy Economics, 25(5), pp.435-457.
20.Hendricks, D., 1997. Evaluation of Value-at-Risk Models Using Historical Data. Economic Policy Review, 2(1).
21.Jorion, P., 2001. Value at Risk: The New Benchmark for Managing Financial Risk. Vol. 2. New York: McGraw-Hill.
22.Markowitz, H., 1952. Portfolio Selection. Journal of Finance, 7(1), pp.77-91.
23.Mandelbrot, B.B., 1997. The Variation of Certain Speculative Prices. In Fractals and Scaling in Finance. Springer, New York, NY. pp.371-418
24.McNeil, A.J. and Frey, R., 2000. Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach. Journal of Empirical Finance, 7(3-4), pp.271-300.
25.Mittnik, S. and Paolella, M.S., 2000. Conditional Density and Value‐at‐Risk Prediction of Asian Currency Exchange Rates. Journal of Forecasting, 19(4), pp.313-333.
26.Nelson, D.B., 1991. Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica: Journal of the Econometric Society, pp.347-370.
27.Pritsker, M., 1997. Evaluating Value at Risk Methodologies: Accuracy Versus Computational Time. Journal of Financial Services Research, 12(2-3), pp.201-242.
28.Politis, D.N., 2004. A Heavy-Tailed Distribution for ARCH Residuals with Application to Volatility Prediction.
29.van den Goorbergh RW, Vlaar PJ. Value-at-Risk Analysis of Stock Returns Historical Simulation, Variance Techniques or Tail Index Estimation?. De Nederlandsche Bank NV; 1999 Mar.