Ising模型在金融市场价格构成中的应用
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摘要
主要利用Sznajd简化的伊辛模型,模拟中国证券市场单个股票的股价形成机制,并与实际个股的收益率及其统计性质进行比较。通过比较模拟收益率和实际收益率,发现Sznajd模型所给的价格形成机制和实际证券市场具有一致的统计性质,如都有相同的尖峰厚尾等普遍特征。通过与Sznajd模型模拟数据的比较,还发现个股正负收益率的统计性质存在明显的不对称性,表明投资人在正负收益率上的交易偏好存在差异。研究表明利用Sznajd模型对证券市场的研究具有重要的应用价值。
In this paper,the formation mechanism of individual stock price in the securities market of China is simulated by applying the Sznajd simplified Ising model. The simulated results are also compared with both the return rate of the real stock and the statistical properties. The results showthat the price formation mechanism in the Sznajd model presents the similar characteristics such as the excess kurtosis and heavy-tail etc.,by comparing the statistical properties of the simulating data and the return rate of the real stock market. It is also found that the statistical nature of the positive and negative return rates of individual stocks is obvious asymmetry,which represents that the trading preferences of investors on positive and negative returns are various. The Sznajd model has important application value to the study of the financial market.
In this paper,the formation mechanism of individual stock price in the securities market of China is simulated by applying the Sznajd simplified Ising model. The simulated results are also compared with both the return rate of the real stock and the statistical properties. The results showthat the price formation mechanism in the Sznajd model presents the similar characteristics such as the excess kurtosis and heavy-tail etc.,by comparing the statistical properties of the simulating data and the return rate of the real stock market. It is also found that the statistical nature of the positive and negative return rates of individual stocks is obvious asymmetry,which represents that the trading preferences of investors on positive and negative returns are various. The Sznajd model has important application value to the study of the financial market.
引文
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[12]涂育松,李晓,邓敏艺,等.一维Sznajd舆论模型相变的研究[J].广西师范大学学报(自然科学版),2005,23(3):5-8.
[13]李其德,王军.基于Ising模型的股票价格统计特征及模拟[J].北京交通大学学报,2007,31(6):81-83.
[14]金华,陆继宗.Ising模型在经济物理学中的应用[J].上海电机学院学报,2008,11(1):66-70.
[15]边宽江,程波,王蕾蕾.收益分布尖峰厚尾问题的统计检验[J].统计与决策,2009(7):83-85.
[16]赵鹏举,刘玉敏.反馈交易与证券市场收益的尖峰厚尾特征[J].系统工程,2009,27(2):7-13.
[2]PETER E E.Chaos and oder in the capital market[M].NewYork:John Wiley&Sons,1991.
[3]CHALLER D,MARSILI M,ZHANG Y C.Modeling market mechanism with minority game[J].physica A,2000,276(1):284-315.
[4]WERON K S,WERON R.A simple model of price formation[J].International Journal of M odern Physics C,2002,13(1):115-123.
[5]ISING E.Eeitrag zur therie des ferromagnetismus[J].Z Phys,1925,31(1):253-258.
[6]H OSBORN.Modern theory of critical phenomena[J].Physics Bulletin,1977,28(4):183.
[7]KRAMERS H A,WANNIER G H.Statistics of the two-dimensional ferromagnet.part I[J].Physical Review,1941,60(3):252-262.
[8]张祥,陈冬保,陈武鸣.二维伊辛模型蒙特卡罗模拟[J].南京大学学报(自然科科学版),1997(1):137-141.
[9]张志东.伊辛模型的研究进展简介[J].自然杂志,2008,30(2):94-98+101.
[10]郭松青.三维蜂穴Ising模型的磁矩[J].沈阳航空工业学院学报,2000,17(3):54-56.
[11]SILVA L,STAUFFER D.Ising-correlated clusters in the cont-bouchaud stock market model[J].Physica A,2001,294(1):235-238.
[12]涂育松,李晓,邓敏艺,等.一维Sznajd舆论模型相变的研究[J].广西师范大学学报(自然科学版),2005,23(3):5-8.
[13]李其德,王军.基于Ising模型的股票价格统计特征及模拟[J].北京交通大学学报,2007,31(6):81-83.
[14]金华,陆继宗.Ising模型在经济物理学中的应用[J].上海电机学院学报,2008,11(1):66-70.
[15]边宽江,程波,王蕾蕾.收益分布尖峰厚尾问题的统计检验[J].统计与决策,2009(7):83-85.
[16]赵鹏举,刘玉敏.反馈交易与证券市场收益的尖峰厚尾特征[J].系统工程,2009,27(2):7-13.