Table Of ContentLimit 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
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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
