A stochastic model for order book dynamics订货簿动态的随机模型

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1、AstochasticmodelfororderbookdynamicsRamaCont,SashaStoikov,RishiTalrejaIEORDept,ColumbiaUniversity,NewYorkrama.cont@columbia.edu,sashastoikov@gmail.com,rt2146@columbia.eduWeproposeastochasticmodelforthecontinuous-timedynamicsofalimitorderbook.Themodelstrikesabalancebetweentwodesirab

2、lefeatures:itcaptureskeyempiricalpropertiesoforderbookdynamicsanditsanalyticaltractabilityallowsforfastcomputationofvariousquantitiesofinterestwithoutresortingtosimulation.Wedescribeasimpleparameterestimationprocedurebasedonhigh-frequencyobservationsoftheorderbookandillustratethere

3、sultsondatafromtheTokyostockexchange.UsingLaplacetransformmethods,weareabletoefficientlycomputeprobabilitiesofvariousevents,conditionalonthestateoftheorderbook:anincreaseinthemid-price,executionofanorderatthebidbeforetheaskquotemoves,andexecutionofbothabuyandasellorderatthebestquotes

4、beforethepricemoves.Comparisonwithhigh-frequencydatashowsthatourmodelcancaptureaccuratelytheshorttermdynamicsofthelimitorderbook.Keywords:Limitorderbook,financialengineering,Laplacetransforminversion,queueingsystems,simulation.1Cont,StoikovandTalreja:Astochasticmodelfororderbookdyna

5、mics2Contents1Introduction32Acontinuous-timemodelforastylizedlimitorderbook42.1Limitorderbooks.....................................42.2Dynamicsoftheorderbook................................53Parameterestimation63.1Descriptionofthedataset.................................63.2Estimati

6、onprocedure...................................74Laplacetransformmethodsforcomputingconditionalprobabilities84.1Laplacetransformsandfirst-passagetimesofbirth-deathprocesses..........94.2Directionofpricemoves..................................104.3Executinganorderbeforethemid-pricemove

7、s.....................124.4Makingthespread.....................................135NumericalResults155.1Longtermbehavior....................................155.1.1Steadystateshapeofthebook..........................155.1.2Volatility......................................155.2Condition

8、aldistributions...........