证券成交量价的行为是否像是一种几率波

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-1-证券成交量/价的行为是否像是一种几率波石磊磊a,b,c2005年10月17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京100738E-mail:Shileilei8@yahoo.com.cn或leilei.shi@hotmail.com摘要:考虑到在股票市场中成交金额对成交量和价格波动存在某种约束关系本文作者通过成交金额来研究成交量与价格波动之间的相互关系我们发现随着交易时间的延长累计交易量在交易价格区间逐渐地在成交价格平均值附近呈现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为了解释这种量价行为我们运用物理学的方法提出了成交能量关系假说推导出一个不显含时间变量的证券成交量/价几率波方程并且得到两组解析的成交量随价格变化的分布函数通过实证检验我们证明了在股票市场中存在着相干特性初步验证了该模型的有效性成交量价的行为像是一种几率波这样我们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JEL分类G12;D30;D40关键词价格波动成交量峰化成交量/价行为相干几率波-2-DoesSecurityTransactionVolume-PriceBehaviorResembleAProbabilityWave?LeileiShia,b,c(October17,2005)aDepartmentofSystemsScience,SchoolofManagement,BeijingNormalUniversity,Beijing100875,ChinabDepartmentofModernPhysics,UniversityofScienceandTechnologyofChina,Hefei230026,ChinacAgents,Generali-ChinaLifeInsuranceCo.Ltd.(BeijingBranch),Beijing100738,ChinaE-mailaddresses:Shileilei8@yahoo.com.cn,or,leilei.shi@hotmail.comAbstractMotivatedbyhowtransactionamountconstraintradingvolumeandpricevolatilityinstockmarket,we,inthispaper,studytherelationbetweenvolumeandpriceifamountoftransactionisgiven.Wefindthataccumulativetradingvolumegraduallyemergesakurtosisnearthepricemeanvalueoveratradingpricerangewhenittakesalongertradingtime,regardlessofactualpricefluctuationpath,timeseries,ortotaltransactionvolumeinthetimeinterval.Toexplainthevolume-pricebehavior,we,intermsofphysics,proposeatransactionenergyhypothesis,deriveatime-independenttransactionvolume-priceprobabilitywaveequation,andgettwosetsofanalyticalvolumedistributioneigenfunctionsoveratradingpricerange.Byempirictest,weshowtheexistenceofcoherenceinstockmarketanddemonstratethemodelvalidationatthisearlystage.Thevolume-pricebehaveslikeaprobabilitywave.Thus,weattempttoofferaunified,micro,anddynamicwavetheoryonpricevolatilityprobabilityinfinancialmarket.JELClassifications:G12;D30;D40Keywords:Pricevolatility;Volumekurtosis;Volume-pricebehavior;Coherence;Probabilitywave-3-1.IntroductionAlthoughtherearemanytradingpricemodelsinfinancialmarket,noneofthemhastheexplicitpriceformationmechanismthatisexpressedbyananalyticalexpression.Fama[1]andRoss[2]launchedefficientmarkethypothesisandarbitragepricingtheory,respectively,basedonrationaltradingassumption.BlackandScholes[3],togetherwithMerton[4],derivedaBlack-Scholes-MertonmodelintermsofSamuelson’slog-normalprocessoreconomicBrownianmotion[5]thatcouldbetracedtoBachelier’sdissertationregardinganoptionpricingproblem[6].Inaddition,Engle[7]formulatedARCHmodel,whichwaslaterdevelopedtoGARCHmodelbyBollerslev[8],toestimatepricevolatilityerrorornonlinearitem.Inrecentyears,someeconophysicistsbeginusingformulationinphysicstodevelopassetpricingmodelsinfinancialmarket.Forexample,McCauleyandGunaratne[9]showedhowtheFokker-Plankformulationoffluctuationscanbeusedwithalocalvolatilitytogenerateanexponentialdistributionforassetreturn.Inthepast20years,therewasagrowingbodyofresearchstudyingpriceandvolume.Gallantetal.[10]undertookacomprehensiveinvestigationofpriceandvolumeco-movementusingdailyNewYorkStockExchangedatafrom1928to1987.Gervaisetal.[11]claimedtheexistenceofhigh-volumereturnpremiuminstockmarket.Moreover,Zhang[12],aneconophysicist,presentedanargumentforasquare-rootrelationshipbetweenpricechangesanddemand.Overthelastfewyears,spinmodelsareusedinstudyingpriceandvolumeasthemostpopularmodelsineconophysics[13].Plerouetal.[14]appliedaspinmodelandempiricallyaddressedhowstockpricesrespondtochangesindemand.Theyfoundthatlargepricefluctuationsoccurwhendemandisverysmall.AusloosandIvanova[15]studiedpriceandvolumebyintroducingthenotionofageneralizedkineticenergy.Ageneralizedmomentumisalsoborrowedfromclassicalmechanics.Itisdefinedastheproductofnormalizedtransactionvolumetimestheaveragerateofpricechangeduringapricemovingaverageperiod.Theyemphasizedattheclosethattheseconceptsmightalsoserveinadynamicequationframework.WangandPandey[16]followedthesameterminologywithsomewhatdifferentdefinitions.Theydefinedtradingmomentumastheproductofrelativepricevelocityandatime-dependent“mass”,anormalizedtradingvolumeinatimeinterval,i.e.thevolumeliquidity.However,traditionalliteratureonpriceandvolumemainlyfocusesonthecorrelationbetweenreturnandtotalvolume(overatradingpricerange)inagiventimeinterval.Somescholarsattemptedtoexplainthebehaviorofpriceandvolume.AdmatiandPfleiderer[17]developedatheoryinwhichconcentrated-tradingpatternsariseendogenouslyasaresultofthestrategicbehaviorofliquiditytradersandinformedtraders.Wang[18]usedICAPMtoestablishatheoreticallinksbetweenpricesandvolume.Econophysicists,forexample,Gabaixetal.[19]proposedatheorytoprovideaunifiedwaytounderstandthepower-lawtaileddistributionsofreturnandvolume,thenon-normaldistributionsthathavebeencaughtmuchattentionbyeconophysicistssinceMandelbrot’sfinding[20].Butcurrenttheoriescreditedthecorrelationbetweenpriceandvolumetoavarietyoffactors,forexamples,(optimal)tradingmotiveandinformationqualityetc.“Whatissurprisingishowlittlewereallyknowabouttradingvolume”[21].Soros[22]guessed:Innaturalsciences,thephenomenonmostsimilartothatinfi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