機率密度函數風險值模型在臺灣店頭市場之實證研究

The Study on Value at Risk of Probability Density Functions in Taiwan OTC Market

10.6656/MR.2005.24.2.CHI.77

邱臙珍(Yen-Chen Chiu)；莊益源(I-Yuan Chuang)；王祝三(C. Edward Wang)

風險值 ； 機率密度函數 ； 核心密度函數 ； 極值理論 ； Value at Risk ； Probability Density Function ； Kernel Density Function ； Extreme Value Theory

管理評論

24卷2期（2005 / 04 / 01）

77 - 109

繁體中文

本研究以捕捉機率密度的風險值模型為研究對象，我們應用Knight，Satchell and Tran (1995)的Double-gamma分配來計算風險值，並比較EWMA、混合常態分配、t分配、高斯核心密度函數、指數核心密度函數及極值分配的GEV與GPD分配等共八種模型的績效。實證的對象是臺灣83個店頭市場公司股票、等權投資組合及模擬投資組合。績效評比是以二項分配、條件涵蓋法與分配預測模型進行檢定。實證的結果顯示，在估計單日個股風險值方面，EWMA的表現最佳；在估計多日個股風險值方面，以Student's t分配的表現較為出色；而本文首度應用的Double-gamma分配在處理模擬投資組合風險值時其績效最優異。

This paper evaluates different probability density functions in the application of Value-at-Risk measures. We apply Knight, Satchell and Tran's (1995) Double-gamma distribution to measure VaR and examine models including EWMA, Mixture Normal, Student's t, Gaussian Kernel, Epanechnikov Kernel and Extreme Value distributions. The data include 83 Taiwan OTC stocks, equal weighted portfolio and simulated portfolio. The tests based on binomial test, conditional coverage and distribution forecasts show that the EWMA performs best for one-day holding period and the Student's t model tends to outperform the others for five-day holding period. In addition, the Double-gamma model also performs well for simulated portfolio.

1. Adams, J.,C. Montesi(1995).Financial Accounting Standard Board.Newark:Connecticut.
2. Bond, A.(2000).mimeo.Cambridge, UK:Department of Land Economy, University of Cambridge.
3. Butler, S.,B. Schachter(1998).Estimating Va1ue-at-Risk with a Precision Measure by Combining Kernel Estimation with Historical Simulation.Review of Derivatives Research,1,371-390.
4. working paper
5. Chou, P. H.,S. Chib(1995).Estimating the Optimal Hedge Ratio under Price limits: A Bayesian Approach Using Gibbs Sampler.Taiwan:Department of Finance, National Central University.
6. Christoffersen, P. F.(1998).Evaluating Interval Forecasts.International Economic Review,39,841-862.
7. Crnkovic, C.,J. Drachman(1996).Quality Control.Risk,9,138-143.
8. Danielsson, J.,G. de Vries,P. Embrechts (ed.)(2000).Value-at-Risk and Extreme Returns.Extremes and Integrated Risk Management.
9. Danielssonv J.,G. de Vries(1997).Tail Index and Quantile Estimation with Vary High Frequency Data.Journal of Empirical Finance,4,241-257.
10. Dowd, K.(2002).Measuring Market Risk.New York:John Wiley and Sons.
11. Duffie, D.,J. Pan(1997).An Overview of Value at Risk.Journal of Derivatives,Spring,7-49.
12. Gnedenko, B.(1943).Sur la Distribution Limite du Terme Maximum d'une Série Aléatoric.Annals of Mathematics,44,423-453.
13. Hendricks, D.(1996).Economic Policy Review.New York:Federal Reserve Bank.
14. J. P. Morgan(1996).RiskMetrics Technical Document.New York:
15. Jorion, P.(2000).Value at Risk.McGraw-Hill.
16. Kim, K. A.,S. G. Rhee(1997).Price Limit Performance: Evidence from Tokyo Stock Exchange.Journal of Finance,52,885-901.
17. Knight, L.,S. Satchell,C. Tran(1995).Statistical Modelling of Asymmetric Risk in Asset Returns.Applied Mathematical Finance,2,155-172.
18. Kupiec, P.(1995).Techniques for Verifying the Accuracy of Risk Measurement Models.Journal of Derivatives,3,73-84.
19. working paper
20. Longin, F.(2000).From Value at Risk to Stress Testing: the Extreme Value Approach.Journal of Banking and Finance,24,1097-1130.
21. Lopez, J.(1999).Methods for Evaluating Value-at-Risk Estimates.Economic Review,2,3-17.
22. Mao, J. C. T.(1970).Survey of Capital Budgeting: Theory and Practice.Journal of Finance,25,349-360.
23. Markowitz, H. M.(1959).Portfolio Selection: Efficient Diversification of Investment.New York:John Wiley and Sons.
24. McNeil, A.(1997).Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory.ASTIN Bulletin,27,117-137.
25. McNeil, A.(1997).The Peaks Over Thresholds Method for Estimating High Quantiles of Loss Distributions.XXVIIth International ASTIN Colloquium
26. McNeil, A.,R. Frey(2000).Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach.Journal of Empirical Finance,271-300.
27. Parzen, E.(1979).Nonparametric Statistical Data Modeling.Journal of the American Statistical Association,74,105-131.
28. Pearson, N.,C. Smithson(2000).Beyond VaR.Risk,12,85-87.
29. Praetz P. D.(1972).The Distribution of Share Price Changes.Journal of Business,45,49-55.
30. Press, W.,S. Teukolsky, W. Vetterling,B. Flannery(1992).Numerical Recipes in C.Cambridge University Press.
31. Sheather, J.,J. Marron(1990).Kernel Quantile Estimators.Journal of the American Statistical Association,85,410-416.
32. Silvapulle, P.,C. Granger(2001).Large Returns, Conditional Correlation and Portfolio Diversification: A Value-at-Risk Approach.Quantitative Finance,542-551.
33. Silverman, B.(1986).Density Estimation for Statistics and Data Analysis.London:Chapman and Hall.
34. Smith, R.(1985).Maximum Likelihood Estimation in a Class of Non-regular Cases.Biometrika,72,67-90.
35. Sutrick, K. H.(1993).Reducing the Bias in Empirical Studies Due to Limit Moves.Journal of Futures Markets,13,527-543.
36. Tsay, R.(2000).Analysis of Financial Time Series.New York:John Wiley & Sons.
37. Venkataraman, S.(1997).Value at Risk for a Mixture of Normal Distributions: the Use of Quasi-Bayesian Estimation Techniques.Economic Perspectives,March/April,2-13.
38. Yang, S.(1985).A Smooth Nonparametric Estimator of a Quantity Function.Journal of the American Statistical Association,80,1000-1011.
39. 高志明(1999)。碩士論文(碩士論文)。銘傳大學金融系。
40. 莊益源,林文昌,徐嘉彬,邱臙珍(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.
41. 魏志安(2002)。碩士論文(碩士論文)。中正大學數學系。