應用Copula-FHS模型於國際投資組合風險值評估

Applying Copula Based FHS Model for the Estimation of International Portfolio Value-at-Risk

李沃牆(Wo-Chiang Lee)；曾智業(Jhih-Ye Zeng)；彭敏瑜(Miin-Yu Peng)

Copula函數 ； 極值理論 ； GARCH模型 ； FHS ； 風險值 ； Copula Function ； Extreme Value Theory ； GARCH Model ； FHS ； VaR

中原企管評論

11卷1期（2013 / 04 / 01）

81 - 110

繁體中文

本文運用修正後的歷史模擬法（Filtered Historical Simulation, FHS）、GARCH-EVT模型和以Copula為基礎的FHS模型（Copula Based FHS Model）三種方法評估國際投資組合之風險值；並進一步應用Kupiec（1995）的概似比檢定（Likelihood Ratio Test, LR Test）和均方誤差法（Root Mean Squared Error, RMSE）評估風險值模型的績效。由實證結果可知次貸危機發生後，各國股價指數之間的關聯性結構具有顯著的變動，使得國際投資組合不再具有風險分散效果。另由概似比檢定可知，無論是在金融危機前後，FHS模型有較佳的績效。另一方面，相較於傳統的線性結構，非線性關聯結構的Copula函數可以相對準確地預測風險值。

The article applies Filtered Historical Simulation, GARCH-EVT model and Copula Based FHS model to calculate the Value at Risk (VaR) of international portfolio. We conduct the Kupiec (1995)'s LR test and use Root Mean Squared Error (RMSE) to evaluate the performance of all VaR models. The empirical results show that the relationship among international stock indexes has significant varying such that international portfolio didn't have diversified effect of risk. The FHS model has the better performance no matter before or during the financial crisis through the LR test. On the other side, comparing with traditional linear structure, the nonlinear structure is relatively correct on VaR forecasting.

1. Patton, A. J., 2002, Modeling Time-Varying Exchange Rate Dependence Using the Conditional Copula. Working Paper.
2. Butler, K. C.,Joaquin, D. C.(2002).Are the Gains from International Portfolio Diversification Exaggerated? The Influence of Downside Risk in Bear Markets.Journal of International Money and Finance,21(7),981-1011.
3. Chan, K. F.,Gray, P.(2006).Using Extreme Value Theory to Measure Value-at-Risk for Daily Electricity Spot Prices.International Journal of Forecasting,22(2),283-300.
4. Chen, M. Y.,Chen, J. E.(2005).Application of Quantile Regression to Estimation of Value at Risk.Review of Financial Risk Management,1(2),1-15.
5. Chollete, L.,Heinen, A.,Valdesogo, A.(2009).Modeling International Financial Returns with a Multivariate Regime-Switching Copula.Journal of Financial Econometrics,7(3),437-480.
6. Chow, G. C.(1960).Tests of Equality between Sets of Coefficients in Two Linear Regressions.Econometrica,28(3),591- 605.
7. Cruz, M. G.(2002).Modeling, Measuring, and Hedging Operational Risk.New York, NY:John Wiley & Sons.
8. Eun, C. S.,Resnick, B. G.(1988).Exchange Rate Uncertainty, Forward Contracts, and International Portfolio Selection.Journal of Finance,43(1),197-215.
9. Ghorbel, A.,Trabelsi, A.(2009).Measure of Financial Risk Using Conditional Extreme Value Copulas with EVT Margins.Journal of Risk,11(4),51-85.
10. Gruble, H.(1968).International Diversified Portfolios: Welfare Gains and Capital Flows.American Economic Review,58(5),1299-1314.
11. Hill, B. M.(1975).A Simple General Approach to Inference about the Tail of a Distribution.Annals of Statistics,3(5),1163-1173.
12. Hull, J.,White, A.(1998).Incorporating Volatility Updating into the Historical Simulation Method for Value-at-Risk.Journal of Risk,1(1),5-19.
13. Jorion, P.(2000).Value at Risk: The New Benchmark for Managing Financial Risk.Chicago, IL:McGraw-Hill.
14. Koenker, R.,Bassett, G., Jr.(1978).Regression Quantiles.Econometrica,46(1),33-50.
15. Kupiec, P. H.(1995).Techniques for Verifying the Accuracy of Risk Measurement Models.Journal of Derivatives,3(2),73-84.
16. Lee, E. C.,Lin, H. N.(2011).Portfolio Value at Risk with Copula-ARMAX-GJR-GARCH Model: Evidence from the Gold and Silver Futures.African Journal of Business Management,5(5),1650-1662.
17. Luciano, E.,Marena, M.(2002).Portfolio Value at Risk Bounds.International Transactions in Operational Research,9(5),629-641.
18. McNeil, A. J.,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),271-300.
19. Peng, Y.,Ng, W. L.(2012).Analysing Financial Contagion and Asymmetric Market Dependence with Volatility Indices via Copulas.Annuals of Finance,8(1),49-74.
20. Schweizer, B.,Wolff, E. F.(1981).On Nonparametric Measures of Dependence for Random Variables.Annals of Statistics,9(4),879-885.
21. Sklar, A.(1959).Fonctions de Répartition à N Dimensions et Leurs Marges.Publications de l'Institut de statistique de l'Université de Paris,8,229-231.
22. Thomas, S.,Sarma, M.,Shah, A.(2003).Selection of Value-at-Risk Models.Journal of Forecasting,22(4),337-358.
23. Wang, K.,Chen, Y. H.,Huang, S. W.(2011).The Dynamic Dependence Between the Chinese Market and Other International Stock Markets: A Time-Varying Copula Approach.International Review of Economics and Finance,20(4),654-664.
24. 李沃牆、李莠苓(2011)。應用 Copula-GJR-GARCH 模型於黃金與白銀期貨之避險。臺灣期貨與衍生性商品學刊，12，28-65。
25. 杜玉振、涂登才、魏郁珣(2008)。買入和放空交易部位最適風險值模型之研究─以股票、商品及外匯市場為例。2008 年銘傳大學國際學術研討會，桃園:
26. 周裕峰(2001)。碩士論文(碩士論文)。銘傳大學財務金融研究所。
27. 詹正邵(2011)。碩士論文(碩士論文)。逢甲大學統計與精算研究所。
28. 賴奕豪、江福松、林煌傑(2010)。極端報酬下亞洲股市之蔓延效果：應用 Copula 分析法。經濟與管理論叢，6(2)，247-270。