证券市场对数收益率的广义偏斜t分布
Generalized Skew t Distribution of Log-Return Rate in Stock Market

作者: 杨 昕 :桂林航天工业学院,数理部,桂林;

关键词: 证券指数对数收益率广义偏斜t分布Stock Index Log-Return Rate Generalized Skewed t Distribution

摘要:
本文的主要问题是研究证券市场中对数收益率的分布特征。对上证指数、深证成指、工业指数、地产指数、消费服务和食品饮料等6个指数一个年度的交易日的收盘数据,利用统计检验方法进行实证分析,分析结果表明:证券指数的对数收益率不服从正态分布,具有尖峰、厚尾、偏斜等特征,它们均以较大的概率被接受为服从广义偏斜t分布,所以广义偏斜t分布是研究证券市场对数收益率的合理分布。

Abstract: The main aim of this paper is to study the distribution characteristics of log-return rate in stock market. The closing data of a year trading day of the 6 indexes (the Shanghai composite index, Shenzhen stock index, industrial index, real estate index, consumer services index, and food and beverage index), are done with the empirical analysis by using the statistical methods. Results show that the log-return rates of the stock indexes do not obey the normal distribution, with the characteristics of high peak, heavy tail and skew distribution. And results also show that the log-return rates are with high probability to be accepted as obeying the generalized skew t distri-bution. So the generalized skewed t distribution is a reasonable distribution to research the log-return rate of stock market.

文章引用: 杨 昕 (2014) 证券市场对数收益率的广义偏斜t分布。 统计学与应用, 3, 141-147. doi: 10.12677/SA.2014.34019

参考文献

[1] Duffie, D. and Pan, J. (1997) An overview of value-at-risk. The Journal of Derivatives, 7, 7-49.

[2] Mandelbrot, B. (1963) The variation of certain speculative pricings. Journal of Business, 36, 394-419.

[3] Fama, E.F. (1965) The behavior of stock market prices. Journal of Business, 38, 34-105.

[4] Blattberg, R. and Gonedes, N. (1974) A com-parison of stable and student distributions as statistical models for stock prices. Journal of Business, 47, 244-280.

[5] Cont, R. (2001) Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1, 223- 236.

[6] Seneta, E.(2004) Fitting the variance-gamma model to financial data. Journal of Applied Probability, 1A, 177-187.

[7] Lin, S.K., Wang, R.H. and Fuh, C.D. 2006) Risk management for linear and non-linear assets: A Bootstrap method with importance resampling to evaluate Value-at-Risk. Asia-Pacific Finan Markets, 3, 261-295.

[8] Fergusson, K. and Platen, E. (2006) On the distributional characterization of daily log returns of a world stock index. Applied Mathematical Finance, 13, 19-38.

[9] Wu, L. (2006) Dampened power law: Reconciling the tail behavior of financial security returns. The Journal of Business, 79, 1445-1473.

[10] Klass1, O.S., Biham, O., Levy, M., Malcai, O. and Solomon1, S. (2007) The Forbes 400, the Pareto power-law and efficient markets. The European Phys-ical Journal B, 55, 143-147.

[11] Plerou, V. and Stanley, H.E. (2008) Stock return distributions: tests of scaling and universality from three distinct stock markets. Physical Review E, 77, 037101.1-037101.4.

[12] 刘建元, 刘琼荪 (2007) 基于非对称Laplace分布研究VaR. 统计与决策, 18, 33-35.

[13] 宋丽娟, 杨虎 (2008) 基于APARCH-Laplace模型的VaR和CVaR方法. 统计与决策, 14, 16-19.

[14] 陈晔, 晏小兵, 王跃恒 (2010) 股票投资组合的实证研究. 数学理论与应用, 1, 110-115.

[15] Azzalini, A. (1985) A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171-178.

[16] Nadarajah, S. and Kotz, S. (2007) Skew models I. Acta Applicandae Mathematicae, 98, 1-28.

[17] Nadarajah, S. (2009) The skew logistic distribution. AStA—Advances in Statistical Analysis, 93, 187-203.

分享
Top