亞洲地區風險值模型之績效分析

Performance Evaluation of Value at Risk Models in Asian Market

10.30003/JRM.200503.0001

邱臙珍(Yen-Chen Chiu)；莊益源(I-Yuan Chuang)

風險值 ； 波動率 ； 極值理論 ； Value at Risk ； Volatility ； Extreme Value Theory

風險管理學報

7卷1期（2005 / 03 / 01）

5 - 28

繁體中文

本研究主要是針對能捕捉財務資料具有偏態、峰態、厚尾或變異數具有異質特性的風險值模型，包括屬於機率密度函數模型的混合常態分配、屬於無母數模型的歷史模擬法、BRW與核心密度函數估計法，及能捕捉時變波動率的模型，例如EWMA、HW與動態GEV和GPD等進行評比。實證的對象為亞洲七個國家股價指數，並利用失敗率、二項分配法、條件涵蓋法與漏損函數進行檢定。實證的結果顯示，一般而言，能捕捉時變波動率的模型表現較佳。

The main objective of this paper is to compare and evaluate the performance of the Value-at-Risk methodologies, paying particular attention to models that can capture skewness, kurtosis, fat-tailed characteristics or time-varying volatility. We examine the probability density function of Mixture Normal, Historical Simulation, BRW and Kernel Estimation of the non-parametric models, and the time-varying volatility models including EWMA, HW and conditional Extreme Value Theory (Conditional-GEV and GPD). The backtesting procedures include failure rate, binominal test, conditional coverage test and loss function. In general, models that can capture time-varying volatility perform better.

1. Alexander, C. O.,C. T. Leigh(1997).On the Covariance Matrics Used in Value-at-Risk Models.Journal of Derivatives,4,50-62.
2. Bollerslev, T.(1986).Generalized Autoregressive Conditional Heteroskedasticity.Journal of Econometics,31,307-327.
3. Boudoukh, J.,M. Richardson,R. Whitelaw(1998).The Best of Both Worlds.Risk,11,64-67.
4. Butler, J. S.,B. Schachter(1998).Estimating Value-at-Risk with a Precision Measure by Combining Kernel Estimation with Historical Simulation.Review of Derivatives Research,1,371-390.
5. Byström, H.(2004).Managing Extreme Risks in Tranquil and Volatile Markets Using Conditional Extreme Value Theory.International Review of Financial Analysis,13,133-152.
6. Christoffersen, P. F.(1998).Evaluating Interval Forecasts.International Economic Review,39,841-862.
7. Danielsson, J.,C. G. de Vries(2000).Value-at-Risk and Extreme Returns.Extremes and Integrated Risk Management, Risk Book,8,85-106.
8. Danielsson, J.,C. G. de Vries(1997).Tail Index and Quantile Estimation with Vary High Frequency Data.Journal of Empirical Finance,4,241-257.
9. Duffie, D.,J. Pan(1997).An Overview of Value-at-risk.Journal of Derivatives,Spring,7-49.
10. Engle, R. F.(1982).Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.Econometica,50,987-1008.
11. Fisher, R.,L. Tippett(1928).Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample.Proceedings of the Cambridge Philosophical Society,24,180-190.
12. Gumbel, E.(1958).Statistic of Extremes.New York:Columbia University Press.
13. Hamilton, J.(1994).Time Series Analysis.Princeton University Press.
14. Hendricks, D.(1996).Evaluation of Value-at-Risk Models Using Historical Data.Economic Policy Review,April,36-69.
15. Hull, J.,A. White(1998).Value-al-Risk When Daily Changes in Market Variables are not Normally Distributed.Journal of Derivatives,3,9-19.
16. Hull, J.,A. White(1998).Incorporating Volatility Updating the Historical Simulation Method for Value-at-risk.Journal of Risk,11,9-20.
17. Kupiec, P.(1995).Techniques for Verifying the Accuracy of Risk Measurement Models.Journal of Derivatives,3,73-84.
18. Longin, F.M.(1996).From Value-at-Risk to Stress Testing: the Extreme Value Approach.Journal of Banking & Financ,24,1097-1130.
19. Lopez, J.(1999).Methods for Evaluating Value-at-Risk Estimates.Economic Review,12,3-17.
20. McNeil, A.,R. Frey(2000).Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach.Journal of Empirical Finance,56,271-300.
21. P. Morgan(1996).Risk Metrics Technical Document.New York:
22. Sheather, S. J.,J. S. Marron(1990).Kernel Quantile Estimatiors.Journal of the American Statistical Association,85,410-416.
23. Silvapulle, P.,P. Granger(2001).Large Returns, Conditional Correlation and Portfolio Diversification: A Value-at-Risk Approach.Quantitative Finance,58,542-551.
24. Silverman, B. W.(1986).Density Estimation for Statistics and Data Analysis.London:Chapman and Hall.
25. Venkataraman S.(1997).Value at Risk for a Mixture of Normal Distributions: the Use of Quasi-Bayesian Estimation Techniques.Economic Perspectives.
26. Zangari, P.(1996).Risk Metrics Monitor.New York:
27. 李進生、謝文良、林允永、蔣炤坪、陳達新、盧陽正(2001)。風險管理－風險值(VaR)理論與應用。台北:清蔚科技公司。
28. 高志明(1999)。碩士論文(碩士論文)。銘傳大學金融系。
29. 莊益源、林文昌、徐嘉彬、邱勝珍(2003)。靜態與動態風險值模型績效之比較。證券市場發展季刊，15(4)，107-159。
30. 魏志安(2002)。碩士論文(碩士論文)。中正大學數學系。