证券成交量价的行为是否是一种几率波

-1-证券成交量/价的行为是否是一种几率波石磊磊a,b,c,*2005年8月16日a北京师范大学管理学院系统科学系北京100875b中国科学技术大学近代物理系合肥230026c中意人寿保险有限公司北京分公司代理人北京100738内容摘要本文作者通过成交金额研究股票市场中的成交量与价格之间关系时观察到每只股票全天的成交量即累计交易量在交易价格区间有一种平稳的分布关系随着交易时间的延长累计交易量在交易价格区间逐渐显现出在成交价格均值附近峰化的分布特征这一特征与体系在此间交易价格涨落的路径时间序列或总成交量的大小无关成交量/价的运动表现为一种在线性势产生的中心力的作用下围绕体系某一均衡价格运动的几率波由此作者用物理的方法推导出不显含时间变量的证券成交量/价波动方程并且得到当供求关系变化时两组解析的成交量随价格变化的分布函数用该函数与上证180指数中一些股票在全天真实的成交量随价格的分布进行拟合和检验作者证明了在股票市场中存在一个动态的均衡价格和成交作用力与成交中心力之间的相干特性初步验证了该模型的有效性其结论是无论是静态的供求价格模型还是动态的价格波动随机游走假说都是几率波模型在极端条件下的一种特例这样作者试图提出一个适用于描述金融交易市场的微观和动态的成交价格波动几率的统一理论分类经济物理微观经济学资产定价关键词成交量分布线性势成交量/价几率波方程本征函数动态均衡价格相干*联系人石磊磊手机[phone]电子邮箱[e-mail]或[e-mail]-2-DoesSecurityTransactionVolume/PriceBehaveaProbabilityWave?Shi,Leileia,b,c,*(August16,2005)aDepartmentofSystemsScience,SchoolofManagement,BeijingNormalUniversityBeijing100875,P.R.ChinabDepartmentofModernPhysics,UniversityofScienceandTechnologyofChinaHefei230026,Anhui,P.R.ChinacAgents,Generali-ChinaLifeInsuranceCo.Ltd.(BeijingBranch)Floor6,TowerC2,OrientalPlaza,No.1EastChangAnAve.,Beijing100738,P.R.ChinaAbstractInthispaper,weobserveastationarytransactionvolumedistributionoveratradingpricerangeinintradaytransactionsonindividualstocksbystudyingrelationshipbetweenthevolumeandpriceoftransactionthroughamountoftransactioninstockmarket.Thetransactionoraccumulatedtradingvolumegraduallyemergesakurtosisnearthepricemeanvalueoveratradingpricerangewhenittakesalongertradingtime,regardlessofactualpricefluctuationpath,timeseries,ortotaltransactionvolumeinthetimeinterval.Thevolume/pricebehaveslikeaprobabilitywavetowardanequilibriumprice,drivenbyarestoringforcethatcanberepresentedbyalinearpotential.Intermsofphysics,wederiveatime-independenttransactionvolume/priceprobabilitywaveequationandgettwosetsofanalyticaltransactionvolumedistributioneigenfunctionsoveratradingpricerangewhensupplyordemandquantityvaries.ByfittingandtestingthefunctionswithintradayrealtransactionvolumedistributionsoveratradingpricerangeonaconsiderablenumberofindividualstocksinShanghai180Index,weshowtheexistenceofadynamicequilibriumpriceandcoherencebetweentransactionforceandrestoringforceinstockmarket,anddemonstratethemodelvalidationatthisearlystage.Itconcludesthateitherstaticsupply/demandequilibriumpricemodelorpricerandomwalkhypothesisisanextremeconditionalcaseinthiswavemodel,respectively.Thus,weattempttoofferaunifiedmicroanddynamicwavetheoryonpricevolatilityprobabilityinfinancialmarket.Classification:Econophysics,Microeconomics,AssetPricingKeywords:Transactionvolumedistribution;Linearpotential;Volume/priceprobabilitywaveequation;Eigenfunctions;Dynamicequilibriumprice;Coherence*Correspondingauthor,E-mailaddresses:[e-mail][e-mail](LeileiShi).-3-1.IntroductionItisessentialforustohavebetterunderstandingontradingpricefluctuationandbehavior.Arrow[1]wrote:“FromthetimeofAdamSmith’sWealthofNationsin1776,onerecurrentthemeofeconomicanalysishasbeentheremarkabledegreeofcoherenceamongthevastnumbersofindividualandseeminglyseparatedecisionsaboutthebuyingandsellingofcommodities”Staticsupply/demandequilibriumpricemodeldescribesthatdemandquantityisinverselyproportionaltopricewhereassupplyquantityisproportionalto.Itshowsthatthereexistsanequilibriumpriceatthecrossofasupplycurveandademandcurve,wherethesupplyquantityequalsthedemandquantity(seefigure1).Accordingtoitsqualitativedescription,oversupplyorexcessdemandquantityproducesadrivingforce(Smith’sinvisiblehand)towardanequilibriumpriceautomaticallyinaneconomicsystem.Thissimplemodelhasbeenusedinalmostallofstandardeconomictextbooks[2,3].However,itassumesthatthereisnoactualtradingatalluntilpricereachesequilibriumbecauseofrationalbuyersandsellers.Thisrationalassumptionisnottrueinacompetitiveeconomicsystem[4,5].Forexample,thereisnopricechangeifthereisnoactualtradinginatimeintervalinstockmarket.Actualtradinghappensoveratradingpricerangeinthemarket.Figure1:Isthereanyarestoringforcethatdrivestradingtowardanequilibriumprice0p?Anotherunderlyingassumptioninthestaticmodelderivedfromautilityfunctionisthatpriceisthefunctionofquantity,namely,)(qfp=,wherepispriceandqisquantity.Osborne[6],apioneerineconophysics,observedthat)(qfp=doesnotexistempirically,andthenexplainedwhyconsumerdemandisthefunctionofprice,namely,)(pDq=,astepfunction,andthisisnotinvertible.McCauley[7]showedthat“priceasafunctionofdemanddoesnotexistmathematically,andallequilibriaareunstablewhenproduction/investmentvariablesareallowedtovary”.0pDemandSupplyQuantityPriceRestoringForce-4-Therehavealreadybeensomemodelsdescribingthefluctuationandbehavioroftradingpriceinfinancialmarket.Forexample,Fama[8]andRoss[9]launchedefficientmarkethypothesisandarbitragepricingtheory,respectively,basedonrationaltradingassumption.BlackandScholes[10],togetherwithMerton[11],derivedaBlack-Scholes-MertonmodelintermsofSamuelson’slog-normalprocessoreconomicBrownianmotion[12]thatcouldbetracedtoBachelier’sdissertationregardinganoptionpricingproblem[13].Engle[14]formulatedARCHmodel,whichwaslaterdevelopedtoGARCHmodelbyBollerslev[15],toe