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Limit Order Books PDF

241 Pages·2016·10.926 MB·English
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Limit Order Books A limit order book is essentially a file in a computer that contains all orders sent to the market, with their characteristics such as the sign of the order, price, quantity and a timestamp.Themajorityoforganizedelectronicmarketsrelyonlimitorderbookstostore lists of the interests of market participants in their central computer. A limit order book contains all information available on a specific market and it reflects the way the market movesundertheinfluenceofitsparticipants. This book discusses several models of limit order books. It begins by assessing the empirical properties of data, and then moves on to mathematical models in order to reproduce the observed properties. It finally presents a framework for numerical simulations. It also covers important modelling techniques including agent-based modelling,andadvancedmodellingoflimitorderbooksbasedonHawkesprocesses. The book also provides in-depth coverage of simulation techniques and introduces general, flexible, open source library concepts useful to readers in studying trading strategies in order-drivenmarkets. The book will be useful to graduate students in the field of econophysics, financial mathematicsandquantitativefinance. Thecontentsofthisbookaretaughtbytheauthors at CentraleSupe´lec (France) for a course on “Physics of Markets”. A short course based on the content of this book has been taught at the Graduate School of Mathematical Sciences, University of Tokyo (Japan), and it will be used at the Universite´ Paris Saclay (France)foracourseinquantitativefinance. Fre´de´ric Abergel is a Professor and Director of the Chair of Quantitative Finance, CentraleSupe´lec,France. BeginningasaCNRSscientistatUniversite´ ParisSudOrsay,he acquired several years of industrial experience in investment banking at BNP Paribas, CAI Cheuvreux, Barclays Capital and Natixis CIB. His research interests include financial markets, pricing and hedging of derivatives, quantitative finance and empirical propertiesoffinancialdata. Marouane Anane is a Quantitative Analyst at the BNP Paribas, Paris. His research interests include market making strategies, price dynamics and automated technical analysis. Anirban Chakraborti is a Professor and Dean of the School of Computational and Integrative Sciences, Jawaharlal Nehru University, India. He has held academic/research positions at the Saha Institute of Nuclear Physics, Helsinki University of Technology, BrookhavenNationalLaboratory,BanarasHinduUniversityandtheEcoleCentraleParis. HeisarecipientoftheYoungScientistMedaloftheIndianNationalScienceAcademyin 2009. Hisresearchareasincludeeconophysics,statisticalphysicsandquantumphysics. Aymen Jedidi is a Quantitative Analyst at HSBC Bank, Paris area, France. His research interestsarequantitativeriskmanagementandstochasticorderbookmodelling. Ioane Muni Toke is an Associate Professor and Dean of studies at the Universite´ de la Nouvelle-Cale´donie, New Caledonia. He has held academic/research positions at the Ecole Centrale Paris and University of Texas at Dallas. He has research interests in financial markets modelling and microstructure, quantitative finance, statistical finance, appliedmathematicsandappliedprobability. Physics of Society: Econophysics and Sociophysics This book series is aimed at introducing readers to the recent developments in physics inspired modelling of economic and social systems. Socio economic systems are increasingly being identified as ‘interacting many body dynamical systems’ very much similar to the physical systems, studied over several centuries now. Econophysics and sociophysics as interdisciplinary subjects view the dynamics of markets and society in general as those of physical systems. This will be a series of books written by eminent academicians, researchers and subject experts in the field of physics, mathematics, finance,sociology,managementandeconomics. This new series brings out research monographs and course books useful for the students and researchers across disciplines, both from physical and social science disciplines,includingeconomics. Series Editors: Bikas K. Chakrabarti Mauro Gallegati Professor,SahaInstituteofNuclearPhysics, ProfessorofEconomics,Polytechnic Kolkata,India UniversityofMarche,Italy Alan Kirman H. Eugene Stanley ProfessoremeritusofEconomics,University WilliamFairfieldWarrenDistinguished ofAix MarseilleIII,Marseille,France ProfessorBostonUniversity,Boston,USA Editorial Board Members: Fr(cid:19)ed(cid:19)eric Abergel Hideaki Aoyama ProfessorofMathematics Professor,DepartmentofPhysics, CentraleSupe´lec,Chatenay KyotoUniversity, Malabry,France Kyoto,Japan Anirban Chakraborti Satya Ranjan Chakravarty ProfessorofPhysics ProfessorofEconomics Dean,SchoolofComputationaland IndianStatisticalInstitute,Kolkata,India IntegrativeSciences,JawaharlalNehru Shu-Heng Chen University,NewDelhi,India ProfessorofEconomicsandComputerScience Arnab Chatterjee Director,AI ECONResearchCenter, VisitingScientistofPhysics NationalChengchiUniversity,Taipei,Taiwan SahaInstituteofNuclearPhysics,Kolkata, Cars Hommes India ProfessorofEconomics Domenico DelliGatti AmsterdamSchoolofEconomics,Universityof ProfessorofEconomics AmsterdamDirector,CenterforNonlinear CatholicUniversity,Milan,Italy DynamicsinEconomicsandFinance(CeNDEF), Amsterdam,Netherlands Kausik Gangopadhyay Giulia Iori ProfessorofEconomics ProfessorofEconomics IndianInstituteofManagement,Kozhikode, SchoolofSocialScience,CityUniversity, India London,UnitedKingdom Taisei Kaizoji Kimmo Kaski ProfessorofEconomics ProfessorofPhysics DepartmentofEconomicsandBusiness, Dean,SchoolofScience,AaltoUniversity, InternationalChristianUniversity,Tokyo,Japan Espoo,Finland J(cid:19)anos Kert(cid:19)esz Akira Namatame ProfessorofPhysics ProfessorofComputerScienceand CenterforNetworkScience,CentralEuropean EconomicsDepartmentofComputer University,Budapest,Hungary Science,NationalDefenseAcademy, Parongama Sen Yokosuka,Japan ProfessorofPhysics Sitabhra Sinha UniversityofCalcutta,Kolkata,India ProfessorofPhysics Victor Yakovenko InstituteofMathematicalScience,Chennai, ProfessorofPhysics India UniversityofMaryland,CollegePark,USA Physics of Society: Forthcoming Titles (cid:15) Macro Econophysics: New Studies on Economic Networks and Synchronization by Yoshi Fujiwara, Hideaki Aoyama, Yuichi Ikeda, Hiroshi Iyetomi, Wataru Souma, Hiroshi Yoshikawa (cid:15) Interactive Macroeconomics: Stochastic Aggregate Dynamics with Heterogeneous and InteractingAgentsbyMauroGallegati,CorradoDiGuilmiandSimoneLandini (cid:15) A Statistical Physics Perspective on Socio Economic Inequalities by Victor Yakovenko and ArnabChatterjee Physics of Society: Econophysics and Sociophysics Limit Order Books Fre´de´ric Abergel MarouaneAnane AnirbanChakraborti AymenJedidi IoaneMuniToke 4843/24,2ndFloor,AnsariRoad,Daryaganj,Delhi-110002,India CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781107163980 ⃝c Authors2016 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2016 PrintedinIndia AcataloguerecordforthispublicationisavailablefromtheBritishLibrary ISBN978-1-107-16398-0Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy ofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication, anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. Contents Figures xi Tables xv Foreword xvii Preface xix Acknowledgments xxi 1 Introduction 1 PARTONE EMPIRICALPROPERTIESOFORDER DRIVENMARKETS 2 StatisticalPropertiesofLimitOrderBooks: ASurvey 9 2.1 Introduction 9 2.2 TimeofArrivalsofOrders 9 2.3 VolumeofOrders 12 2.4 PlacementofOrders 13 2.5 CancellationofOrders 15 2.6 AverageShapeoftheOrderBook 16 2.7 IntradaySeasonality 18 2.8 Conclusion 19 3 TheOrderBookShapeasaFunctionoftheOrderSize 20 3.1 Introduction 20 3.2 Methodology 20 3.3 TheRegressionModel 22 3.4 Conclusion 28 4 EmpiricalEvidenceofMarketMakingandTaking 29 4.1 Introduction 29 4.2 Re-introducingPhysicalTime 29 4.3 DependencyPropertiesofInter-arrivalTimes 31 viii 4.3.1 Empiricalevidenceofmarketmaking 31 4.3.2 Areciprocaleffect? 33 4.4 FurtherInsightintotheDependencyStructure 35 4.4.1 Thefinestructureofinter-eventdurations: Usinglagged correlationmatrices 37 4.5 Conclusion 41 PARTTWO MATHEMATICALMODELLINGOFLIMITORDERBOOKS 5 Agent-basedModellingofLimitOrderBooks: ASurvey 45 5.1 Introduction 45 5.2 EarlyOrder-drivenMarketModelling: MarketMicrostructureandPolicy Issues 47 5.2.1 Apioneerorderbookmodel 47 5.2.2 Microstructureofthedoubleauction 48 5.2.3 Zero-intelligence 48 5.3 Order-drivenMarketModellinginEconophysics 49 5.3.1 Theorderbookasareaction-diffusionmodel 49 5.3.2 Introducingmarketorders 51 5.3.3 Theorderbookasadeposition-evaporationprocess 53 5.4 EmpiricalZero-intelligenceModels 54 5.5 SomeAnalyticalandMathematicalDevelopmentsinZero-intelligence OrderBookModelling 57 5.6 Conclusion 58 6 TheMathematicalStructureofZero-intelligenceModels 59 6.1 Introduction 59 6.1.1 Anelementaryapproximation: Perfectmarketmaking 59 6.2 OrderBookDynamics 61 6.2.1 Modelsetup: Poissonianarrivals,referenceframeandboundary conditions 61 6.2.2 Evolutionoftheorderbook 64 6.2.3 Infinitesimalgenerator 66 6.2.4 Pricedynamics 67 6.3 ErgodicityandDiffusiveLimit 68 6.3.1 Ergodicityoftheorderbook 69 6.3.2 Large-scalelimitofthepriceprocess 70 ix 6.3.3 Interpretingtheasymptoticvolatility 74 6.4 TheRoleofCancellations 75 6.5 Conclusion 76 7 TheOrderBookasaQueueingSystem 77 7.1 Introduction 77 7.2 ALinkBetweentheFlowsofOrdersandtheShapeofanOrderBook 78 7.2.1 Thebasicone-sidedqueueingsystem 78 7.2.2 Acontinuousextensionofthebasicmodel 80 7.3 ComparisontoExistingResultsontheShapeoftheOrderBook 83 7.3.1 NumericallysimulatedshapeinSmithetal. (2003) 83 7.3.2 EmpiricalandanalyticalshapeinBouchaudetal. (2002) 84 7.4 AModelwithVaryingSizesofLimitOrders 88 7.5 InfluenceoftheSizeofLimitOrdersontheShapeoftheOrderBook 92 7.6 Conclusion 96 8 AdvancedModellingofLimitOrderBooks 97 8.1 Introduction 97 8.2 TowardsNon-trivialBehaviours: ModellingMarketInteractions 97 8.2.1 Herdingbehaviour 98 8.2.2 Fundamentalistsandtrendfollowers 99 8.2.3 Thresholdbehaviour 101 8.2.4 Enhancingzero-intelligencemodels 101 8.3 LimitOrderBookDrivenbyHawkesProcesses 102 8.3.1 Hawkesprocesses 103 8.3.2 Modelsetup 104 8.3.3 Theinfinitesimalgenerator 105 8.3.4 Stabilityoftheorderbook 106 8.3.5 Largescalelimitofthepriceprocess 108 8.4 Conclusion 110 PARTTHREE SIMULATIONOFLIMITORDERBOOKS 9 NumericalSimulationofLimitOrderBooks 113 9.1 Introduction 113 9.2 Zero-intelligenceLimitOrderBookSimulator 113 9.2.1 AnalgorithmforPoissonianorderflows 113 9.2.2 Parameterestimation 115

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