Scaling properties and universality of first-passage time probabilities in financial markets

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1、Scalingpropertiesanduniversalityoffirst-passagetimeprobabilitiesinfinancialmarketsJosepPerell´o,MarioGuti´errez-RoigandJaumeMasoliverDepartamentdeF´ısicaFonamental,UniversitatdeBarcelona.Diagonal647,E-08028Barcelona,SpainFinancialmarketsprovideanidealframeforthestudyofcrossingorfirst-passagetimeev

2、entsofnon-Gaussiancorrelateddynamicsmainlybecauselargedatasetsareavailable.Tick-by-tickdataofsixfuturesmarketsarehereinconsideredresultinginfattailedfirst-passagetimeprobabilities.Thescalingofthereturnwiththestandarddeviationcollapsestheprobabilitiesofallmarketsexamined,andalsofordifferenttimehor

3、izons,intosinglecurves,suggestingthatfirst-passagestatisticsismarketindependent(atleastforhigh-frequencydata).Ontheotherhand,averycloselyrelatedquantity,thesurvivalprobability,shows,awayfromthecenterandtailsofthedistribution,a−1/2hyperbolictdecaytypicalofaMarkoviandynamicsalbeittheexistenceofmem

4、oryinmarkets.ModificationsoftheWeibullandStudentdistributionsaregoodcandidatesforthephenomenologicaldescriptionoffirst-passagetimepropertiesundercertainregimes.Thescalingstrategiesshownmaybeusefulforriskcontrolandalgorithmictrading.PACSnumbers:89.65.Gh,02.50.Ey,05.40.Jc,05.45.TpI.INTRODUCTIONover

5、,intradayalgorithmictradingstrategies[15]ofbuy-ingorsellingagivenassetcouldlearnfromFPTstatis-tics.Computerbasedtradingisthoughttoberespon-Thefirst-passagetime(FPT)ofagivenstochasticpro-sibleforasmuchas73%oftradingvolumeintheUScessisarandomvariablerepresentingtheinstantoftimein2009[16].Yetempiri

6、calFPTprobabilitiesarequitewhentheprocessfirstattainssomepreassigned“criti-unexploredinfinancialmarkets[17,18]althoughtherecal”value.Thestudyofproblemsrelatedtofirst-passagearesomeworksstudyingotherextreme-timestatisticstimehasalongtraditioninmanybranchesofscienceand[11,19–27].engineering[2,3].Inr

7、ecentyears,empiricalaswellastheoreticalanalysisonthiskindofproblemshavegainedabroaderinterest.Thusnewmultidisciplinarycontextslikeionictransportinabacterialporin[4],proteinfold-inginacrowdedcellenvironment[5],epidemicsspread-ingin