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1、?34?6?Vol.34,No.62014?6?Systems Engineering Theory&PracticeJune,2014?:1000-6788(2014)06-1361-08?:F830?:A?1,?1,?2,?3(1.?,?100083;2.?,?100191;3.Department of Economics,University of California,San Diego,La Jolla,CA 92093)?,?.?,?,?,?.?,?,?;?,?,?,?;?,?,?.?;?;?Does herd behavior increase stock price vola
2、tility?LIU Xiang-dong1,LIU Cheng1,LIU Shan-cun2,LU Jia-jun3(1.Dongling School of Economics and Management,University of Science and Technology Beijing,Beijing 100083,China;2.School of Economics and Management,Beihang University,Beijing 100191,China;3.Department of Economics,Universityof California,S
3、an Diego,La Jolla,CA 92093,USA)Abstract Research results have even given the opposite conclusions on whether herd behavior increasestock price volatility.Assume that the change of view for traders buying or selling is mainly affected bytheir cognitive ability for the basic value of stock and other t
4、raders behaviors.This paper constructs amathematical model describing the change of market average investment attitude and stock prices,andanalyzes the stability of the model by using the related theory of discrete dynamic system,and defines thedegree of herding behavior according to whether the fin
5、ancial market is stable.The results indicate that:in mild herding effect interval,stock prices accordingly present periodic micro-amplitude fluctuations;inmoderate herding effect interval,after experiencing a period of damping volatility,stock prices convergenceto equilibrium,and there exists an opt
6、imal degree of herding behavior which encourages the stock price toapproach equilibrium in the fastest speed;in severe herding effect interval,stock prices irrationally sharplyfluctuate in large amplitudes which can lead to severe stock market bubble and the financial crisis.Keywords herd behavior;s
7、tock price volatility;stability of financial market1?,?.?,?,?.?,?.?,?;?,?.?:2012-08-09?:?(71173012,71371023);?(2013M540855)?:?(1985),?,?,?,?,?:?;?(1967),?,?,?,?,?:?;?(1964),?,?,?,?,?:?;?(1990),?,?,?,?:?.1362?34?,?.?.?,Scharfstein?1?,?()?,?.Lux2?,?,?,?,?.Avery?3?,?,?.?,?4?,?“?”,?.?5?1999?2003?,?,?,?.
8、?6?2001?12?2004?3?,?,?.?,?,?.?,?,?.?,?.Lakonishok?7?,?,?,?,?.Wermers8?1975?1994?,?,?,?,?.?9?GARCH?,?,?,?.?,?,?.?,?,?,?:?Christie?10?Chang?11?,?12,?13?.?,?,?,?(?).?,?.?,?.?,?.?,?,?.?14?Agent?,?,?.?,?,?,?15.?,?,?16.?,?,?,?.?,?,?,?;?,?,?.?,?.?Lux2,17?,?,?,?6?,?:?1363?.?,?,?,?;?,?;?,?.?,?,?,?,?;?,?,?.?,
9、?:?,?;?,?,?.?:?,?,?,?.2?Lux2,17?,?,?n?.?t?,?i?x(i)t,?i?1?,?x(i)t=1;?i?1?,?x(i)t=1.?,?,?.?,?Xt=?ni=1x(i)t/n.?,?t,?Xt(1,1).?Xt 0,?,?Xt 0?.?(5)?(7),?Xt+1=Xt+v?erXt+(mPt)/v)+erXt(mPt)/v)+?vXt?erXt+(mPt)/v)+erXt(mPt)/v)+?Pt+1=Pt+arctan(Xt+1)(8)3?(8)?.?E=(X,P)?(8)?,?X,P?0=v?erXt+(mPt)/v)+erXt(mPt)/v)+?vXt
10、?erXt+(mPt)/v)+erXt(mPt)/v)+?0=arctan(Xt+1)(9)?Pt?,?.?,?(8)?E=(X,P)=(0,m).?(8)?E=(X,P)?Jacobi?J=?1+2v(r 1)e+2v(r 1)e2e1 2e?(10)?det(J)?J?,tr(J)?J?,?(10)?det(J)=1+2v(r 1)e,tr(J)=1+v(r 1)e e?,?(8)?1 tr(J)+det(J)=2e 01+tr(J)+det(J)=2+2v(r 1)e e 01 det(J)=2v(r 1)e 0(11)?,?,?(11)?,?,(11)?2+2v(r 1)e e 02v
11、(r 1)e 0(12)?(12)?,?E=(X,P)?:?v=e22(r1)e,?Neimark Sacker?r1=0.?1?(8)?,?.?,?E=(X,P),?,?,?.?,?(12)?1 2 e2ve r 1(13)?(13)?,?,?.?,?,?.?:?(8)?,?,?(?,?,?.)?.?(13)?,?(8)?,?.?,?.?,?(8)?,?6?,?:?1365?,?,?,?.4?r?.?,?(X0,P0)?r?,?1?.Flip分叉曲线分叉曲线?稳定区域?1?(8)?1?m?10v?0.5?10?0.3?0.1?1?,?P=m=10?,?E=(X,P)=(0,10).?,?.?
12、,?,?.?,?,?,?.?,?(X0,P0)=(0.05,10.1).4.1?,?,?(13)?,?0.39 r 1.?,?;?0.39?,?1?.?,?,?;?,?,?,?,?;?,?.?,?2?(a)?,?r=0.01?(?),?,?.?(a)?.?,?,?,?,?,?,?,?,?,?.?,?r=0.2?,?2?(b)?,?(a)?,?.?,?.?,?.0510152025303540459.59.79.910.110.310.5tr=0.01Pt（a）0510152025303540459.59.79.910.110.310.5tr=0.2Pt（b）?2?r=0.01,0.2?,?13
13、66?34?,?.?3?(a)?(b)?,?r=0.4?r=0.95?,?,?.?(a)?,?(b)?,?,?.?(b)?r=0.95,?r=1.?,?,?.03060901201509.99.949.9810.0210.0610.1tr=0.4Pt（a）03060901201501802109.859.99.951010.0510.110.15tr=0.95Pt（b）?3?r?0.4?0.95?,?r?1?,?,?.?,?r?,?.?,?.?Kaizoji19,Foroni?20?.?,?,?,?(?4?(a)?(b)?),?.?,?,?,?.030609012015088.599.5101
14、0.51111.512tr=1.1Pt（a）030609012015018021088.599.51010.51111.512tr=1.5Pt(b)?4?r?1.1?1.5?,?4.2?r?(0.39,1)?,?,?.?3?(a)?(b)?,?.?,?,?,?,?.?,?,?,?.?,?2122?,?,?.?.?,?,?r=0.42?0.52?0.62?0.75?0.90?,?.?5?(a)?(b)?,?,?36?18?22?30?75?.?,?,?.?,?5?.?,?,?,?.?,?.?6?,?:?13674.3?,?.?,?.?2?5?,?.?,?,?;?,?,?.?,?,?2?5?,?.
15、?,?,?.?,?,?,?,?.?,?,?,?(?6?).0510152025303540459.99.949.9810.0210.0610.1tr=0.42r=0.52r=0.62Pt(a)01020304050607080909.99.949.9810.0210.0610.1tr=0.75r=0.90Pt(b)?5?r?0.42?0.52?0.62?0.75?0.90?,?榖0?6?,?,?,?.?,?,?;?,?,?,?.?,?,?,?.5?,?,?.?.?:?,?;?,?,?,?,?.?,?,?,?.?,?,?.?1368?34?,?,?.?1 Scharfstein D S,Stei
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