文献类型：期刊文献

英文题名：On the probability distribution of stock returns in the Mike-Farmer model

作者：Gu, G. -F.[1,2,3];Zhou, W. -X.[1,2,3,4,5]

机构：[1]E China Univ Sci & Technol, Sch Sci, Shanghai 200237, Peoples R China;[2]E China Univ Sci & Technol, Sch Sci, Shanghai 200237, Peoples R China;[3]E China Univ Sci & Technol, Res Ctr Econophys, Shanghai 200237, Peoples R China;[4]E China Univ Sci & Technol, Minist Educ, Engn Res Ctr Proc Syst Engn, Shanghai 200237, Peoples R China;[5]Chinese Acad Sci, Res Ctr Fictitious Econ & Data Sci, Beijing 100080, Peoples R China

年份：2009

卷号：67

期号：4

起止页码：585

外文期刊名：EUROPEAN PHYSICAL JOURNAL B

收录：;EI(收录号：20091311981513);WOS:【SCI-EXPANDED(收录号:WOS:000264183000013)】；

基金：This work was partly supported by the National Natural Science Foundation of China (Grant No. 70501011), the Fok Ying Tong Education Foundation (Grant No. 101086), the Program for New Century Excellent Talents in University (Grant No. NCET-07-0288), and the Shanghai Dawn Light Program.

语种：英文

外文关键词：Costs - Investments - Students - Agriculture - Financial markets

摘要：Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven market, which can successfully reproduce the whole distribution of returns, not only the well-known power-law tails, together with several other important stylized facts. There are three key ingredients in the Mike-Farmer (MF) model: the long memory of order signs characterized by the Hurst index H(s), the distribution of relative order prices x in reference to the same best price described by a Student distribution (or Tsallis' q-Gaussian), and the dynamics of order cancelation. They showed that different values of the Hurst index H(s) and the freedom degree alpha(x) of the Student distribution can always produce power-law tails in the return distribution f(r)(r) with different tail exponent alpha(r). In this paper, we study the origin of the power-law tails of the return distribution f(r)(r) in the MF model, based on extensive simulations with different combinations of the left part L(x) for x < 0 and the right part R(x) for x > 0 of f(x)(x). We find that power-law tails appear only when L(x) has a power-law tail, no matter R(x) has a power-law tail or not. In addition, we find that the distributions of returns in the MF model at different timescales can be well modeled by the Student distributions, whose tail exponents are close to the well-known cubic law and increase with the timescale.