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1、TransmissionofInformationandHerdBehavior:anApplicationtoFinancialMarketsV′?ctorM.Egu′?luz1,2,?,Mart′?nG.Zimmermann1,3,?1?InstitutoMediterr′aneodeEstudiosAvanzadosIMEDEA(CSIC-UIB),E-07071PalmadeMallorca(Spain)2CenterforChaosandTurbulenceStudies,TheNielsBohrInstitute,
2、Blegdamsvej17,DK-2100Copenhagen?(Denmark)3DepartamentodeF′?sica,Fac.CienciasExactasyNaturales,UniversidaddeBuenosAires,BuenosAires(Argentina)(February1,2008)Weproposeamodelforstochasticformationofopinionclusters,modelledbyanevolvingnetwork,andherdbehaviortoaccountfo
3、rtheobservedfat-taildistributioninreturnsof?nancial-pricedata.Theonlyparameterofthemodelish,therateofinformationdispersionpertrade,whichisameasureofherdingbehavior.Forhbelow?acriticalhthesystemdisplaysapower-lawdistributionofthereturnswithexponentialcut-off.Howeverf
4、or?h>hanincreaseintheprobabilityoflargereturnsisfound,andmaybeassociatedtotheoccurrenceoflargecrashes.PACSnumbers:87.23.Ge,02.50.Le,05.45.Tp,05.65.+bRecently,therehasbeenasigni?cantinterestinapplica-ofthedistributionremainingclosetothepowerlaw.Inourap-tionsofphysica
5、lmethodsinsocialandeconomicalsciencesproachtheaverageconnectivityc(t)ofthenetworkisdriven[1].Inparticular,theanalysisof?nancialstockmarketpricesbytherumorsinadynamicway,andprovidesanextensiontohavebeenfoundtoexhibitsomeuniversalcharacteristicssim-thestaticpercolatio
6、nmodelproposedbyContandBouchaudilartothoseobservedinphysicalsystemswithlargenumber[11],wheretheaverageconnectivitywasa?xedexternalpa-ofinteractingunits,andseveralmicroscopicmodelshavebeenrameter.We?ndthatthefat-tailsdistributionsareobserveddevelopedtostudythem[2–4].
7、Forexamplethedistributionevenwhenthetime-averagedensityc(t)isfarfromthecriti-oftheso-calledreturns,i.e.thelogarithmicchangeofthemar-calthresholdc?=1foundinRef.[11].ketprice,hasbeenobservedtopresentpronouncedtailslargerThemodel.WeconsiderasystemcomposedbyNagents,than
8、inaGaussiandistribution[2,3,5–7].Severalmodelshaverepresentedbyverticesinanetwork.Thestateofagentlisbeenputforwardwhichphenomenologicallys
