Modeling Chinese stock returns with stable distribution

• Published in: Mathematical and computer modelling Vol. 54; no. 1; pp. 610 - 617
• Main Authors: Xu, Weidong, Wu, Chongfeng, Dong, Yucheng, Xiao, Weilin
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.07.2011; Elsevier
• Subjects: Characteristic function; China; costs and returns; Exact sciences and technology; Lévy measure; Mathematical analysis; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Sample quantile method; Sciences and techniques of general use; Stable distribution; China; Characteristic function; Sample quantile method; Lévy measure; Stable distribution; Applied mathematics; Levy measure; Distribution function; Probability; Stable law; Mathematical model; Computing method; Computer aided analysis
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2011.03.004

In this paper we demonstrate that an α -stable distribution is better fitted to Chinese stock return data in the Shanghai Composite Index and the Shenzhen Component Index than the classical Black–Scholes model. The sample quantile method developed by McCulloch [J.H. McCulloch, Simple consistent estimators of stable distribution parameters, Communications in Statistics-Simulation and Computation 15 (4) (1986) 1109–1136] is used to estimate the α -stable distribution for the Shanghai Composite Index and the Shenzhen Component Index. The empirical results show that the asymmetric leptokurtic features presented in the Shanghai Composite Index and Shenzhen Component Index returns can be captured by an α -stable law.