f3518339-0323-4bb8-9315-f354675d841d20210322084150512naunmdt@crossref.orgMDT DepositInternational Journal of Economics and Statistics2309-068510.46300/9103http://www.naun.org/cms.action?id=567232220213222021910.46300/9103.2021.9https://www.naun.org/cms.action?id=23308Research on Volatility of Return of Chinese Stock-Market Based on Generalized Hyperbolic Distribution FamilyWuLibinDepartment of Statistics and Applied Mathematics, Anhui University of Finance and Economics, ChinaLiuShengyuDepartment of Statistics and Applied Mathematics, Anhui University of Finance and Economics, ChinaGaoJunDepartment of Statistics and Applied Mathematics, Anhui University of Finance and Economics, ChinaFinancial time series often present a nonlinear characteristics, and the distribution of financial data often show fat tail and asymmetry, but this don’t match with the standpoint that time series obey normal distribution of return on assets, etc, which is considered by linear parametric modeling in the traditional linear framework. This paper has a systematic introduction of the definitions of GH distribution family and related statistical characteristics, which is based on reviewing the basic properties of the ARCH/GARCH model family and a common distribution of its disturbance. And select the Shanghai Composite Index and the Shanghai and Shenzhen (CSI) 300 index daily return rate index to estimate volatility model. GH distribution is used for further fitting to disturbance. This is done after take full account of the effective extraction of the model for the disturbance distribution information. The results show that the GH distribution can effectively fitting residuals distribution of the volatility models about series on return rate.3222021322202117https://www.naun.org/main/NAUN/economics/2021/a022015-001(2021).pdf10.46300/9103.2021.9.1https://www.naun.org/main/NAUN/economics/2021/a022015-001(2021).pdfFan Jianqing,Yao Qiwei ， Nonlinear time series [M]. Beijing ， Higher Education Press ， 2005.12. 10.1007/s11408-006-0016-4Alexander J. McNeil, Rudiger Frey, and Paul Embrechts. Quantitative Risk Management. Princeton Series in Finance. Princeton University Press, Princeton, NJ, 2005. p.538 Alexander J. McNeil. Free S-Plus and R library designed to accompany the book quantitative risk management: Concepts, techniques and tools. http://cran.rproject. org/web/packages/QRMlib/index.html, 2005. Eberlein, E. and Keller, U., Hyperbolic distributions in finance, Bernoulli, Vol.1, 1995,pp.281-299. 10.1007/978-3-662-12429-1_12Eberlein, E. and K. Prause. The generalized hyperbolic model:financial derivatives and risk measures. In :H. Geman, D. Madan,S. Pliska, and T. Vorst (Eds.), Mathematical Finance-Bachelier Congress 2000, pp. 245–267. (Springer.Berlin). 10.1098/rspa.1977.0041Barndorff-Nielsen, O. (1977) Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. London, A353, 401–419. Barndorff-Nielsen, O. E. (1978), Hyperbolic Distributions and Distributions on Hyperbolae. Scand. J. Statist., 5:151-157. Ciprian Necula,Modeling Heavy-Tailed Stock Index Returns Using Hyperbolic Distribution. Romanian Journal of Economic Forecasting.2009(2):118-131. WenBo Hu. Calibration of Multivariate Generalized Hyperbolic Distributions Using the EM Algorithm, with Applications in Risk Management, Portfolio Optimization and Portfolio Credit Risk [M].Dissertation for Doctor Degree. The Florida State University College of Arts and Sciences, 2005. Wolfgang Breymann,David Luethi,ghyp:A package on the generalized hyperbolic distribution and its special cases, http://cran.rproject. org/web/packages/ghyp/. Cao Zhi-guang,Wang An-xing,Yang Jun-min, The Test of non-normal Distribution of Stock Returns with Monte Carlo Simulation and The Explanation, Journal of Finance and Economics [J],Vol.10,2005,pp:34-41. Lin Qingquan ， Zhang Jianlong,Financial time series modeling and risk measurement—Based on the generalized hyperbolic distribution [M]. Beijing ，Renmin University of China Press，2010。 Feng Jian-qiang,Wang Fu-xin,A Research On Return Distribution Function, Chinese Journal of Management Science, Vol.11,2003,pp:14-21.