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1、TheThermodynamicsofHighFrequencyMarketsKevinThomasWebsterADissertationPresentedtotheFacultyofPrincetonUniversityinCandidacyfortheDegreeofDoctorofPhilosophyRecommendedforAcceptancebytheDepartmentofOperationsResearchandFinancialEngineeringAdviser:ProfessorCarmonaJune2014cCopyrightbyKevinThomasWebster
2、,2014.Allrightsreserved.AbstractHighFrequencyTrading(HFT)representsanevergrowingproportionofall nancialtransactionsasmostmarketshavenowswitchedtoelectronicorderbooksystems.Thisdissertationproposesanovelmethodologytoanalyzeidiosyncrasiesofthehighfrequencymarketmicrostructureandembedtheminclassicalco
3、ntinuoustimemodels.Themaintechnicalresultisthederivationofcontinuoustimeequationswhichgeneralizetheself- nancingrelationshipsoffrictionlessmarketstoelectronicmarketswithlimitorderbooks.WeuseNASDAQITCHdatatoidentifysigni cantempiricalfeaturessuchaspriceimpactandrecovery,roughpathsofinventoriesandvan
4、ishingbid-askspreads.Startingfromthesefeatures,weidentifymicroscopicidentitieshold-ingonthetradeclock,andthroughadi usionlimitargument,derivecontinuoustimeequationswhichprovideamacroscopicdescriptionofpropertiesoftheorderbook.Theseequationsnaturallydi erentiatebetweentradingvialimitandmarketor-ders
5、.Wegiveseveralapplicationstoillustratetheirimpactandhowtheycanbeusedtothebene tofLowFrequencyTraders(LFTs).Inparticular,optionpricingandmarketmakingmodelsareproposedandsolved,leadingtonewinsightsastotheimpactoflimitordersandmarketordersontradingstrategies.iiiAcknowledgementsFirstandforemost,Iwouldl
6、iketothankmyadviser,ReneCarmona,foracceptingtheresearchproblemIgavemyselfnearlyfouryearsagoandhelpingmestickthroughwithitthroughoutthePhD.Theanglesofattackandtoolswechosechangedfromyeartoyear,buthisinsightfuladviceandpassionstayedconstantandstrong.Researchisneverdonecompletelyinisolation,andIamgra
7、tefultoProfessorsYacineAit-Sahalia,JeanJacodandRamonvanHandelforadviceonlimittheoremsforpathfunctionals,atoolthatendedupbeingcrucialinmydissertation.Profes-sorsMarkusBrunnermeierandPatrickCheridito,bothhelp
