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1、TransmissionofInformationandHerdBehavior:anApplicationtoFinancialMarketsV´ıctorM.Egu´ıluz1,2,⋆,Mart´ınG.Zimmermann1,3,‡1†InstitutoMediterr´aneodeEstudiosAvanzadosIMEDEA(CSIC-UIB),E-07071PalmadeMallorca(Spain)2CenterforChaosandTurbulenceStudies,TheNielsBohrInstitute,
2、Blegdamsvej17,DK-2100CopenhagenØ(Denmark)3DepartamentodeF´ısica,Fac.CienciasExactasyNaturales,UniversidaddeBuenosAires,BuenosAires(Argentina)(February1,2008)Weproposeamodelforstochasticformationofopinionclusters,modelledbyanevolvingnetwork,andherdbehaviortoaccountfo
3、rtheobservedfat-taildistributioninreturnsoffinancial-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,therehasbeenasignificantinterestinapplica-ofthedistributionremainingclosetothepowerlaw.Inourap-tionsofphysica
5、lmethodsinsocialandeconomicalsciencesproachtheaverageconnectivityc(t)ofthenetworkisdriven[1].Inparticular,theanalysisoffinancialstockmarketpricesbytherumorsinadynamicway,andprovidesanextensiontohavebeenfoundtoexhibitsomeuniversalcharacteristicssim-thestaticpercolatio
6、nmodelproposedbyContandBouchaudilartothoseobservedinphysicalsystemswithlargenumber[11],wheretheaverageconnectivitywasafixedexternalpa-ofinteractingunits,andseveralmicroscopicmodelshavebeenrameter.Wefindthatthefat-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
