Modelling empirical features and liquidity resilience in
Transcript Of Modelling empirical features and liquidity resilience in
Modelling empirical features and liquidity resilience in the Limit Order
Book
Efstathios Panayi
A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London.
Department of Computing University College London
May 15, 2015
2
I, Efstathios Panayi, confirm that the work presented in this thesis is my own, except for the parts indicated in my statement of conjoint work. Where information has been derived from other sources, I confirm that this has been indicated in the thesis.
Abstract
The contribution of this body of work is in developing new methods for modelling interactions in modern financial markets and understanding the origins of pervasive features of trading data. The advent of electronic trading and the improvement in trading technology has brought about vast changes in individual trading behaviours, and thus in the overall dynamics of trading interactions. The increased sophistication of market venues has led to the diminishing of the role of specialists in making markets, a more direct interaction between trading parties and the emergence of the Limit Order Book (LOB) as the pre-eminent trading system. However, this has also been accompanied by an increased fluctuation in the liquidity available for immediate execution, as market makers try to balance the provision of liquidity against the probability of an adverse price move, with liquidity traders being increasingly aware of this and searching for the optimal placement strategy to reduce execution costs.
The varying intra-day liquidity levels in the LOB are one of the main issues examined here. The thesis proposes a new measure for the resilience of liquidity, based on the duration of intra-day liquidity droughts. The flexible survival regression framework employed can accommodate any liquidity measure and any threshold liquidity level of choice to model these durations, and relate them to covariates summarising the state of the LOB. Of these covariates, the frequency of the droughts and the value of the liquidity measure are found to have substantial power in explaining the variation in the new resilience metric. We have shown that the model also has substantial predictive power for the duration of these liquidity droughts, and could thus be of use in estimating the time between subsequent tranches of a large order in an optimal execution setting.
A number of recent studies have uncovered a commonality in liquidity that extends across markets and across countries. We outline the implications of using the PCA regression approaches that have been employed in recent studies through synthetic examples, and demonstrate that using such an approach for the study of Euro-
Abstract
4
pean stocks can mislead regarding the level of liquidity commonality. We also propose a method via which to measure commonality in liquidity resilience, using an extension of the resilience metric identified earlier. This involves the first use of functional data analysis in this setting, as a way of summarising resilience data, as well as measuring commonality via functional principal components analysis regression.
Trading interactions are considered using a form of agent-based modelling in the LOB, where the activity is assumed to arise from the interaction of liquidity providers, liquidity demanders and noise traders. The highly detailed nature of the model entails that one can quantify the dependence between order arrival rates at different prices, as well as market orders and cancellations. In this context, we demonstrate the value of indirect inference and simulation-based estimation methods (multi-objective optimisation in particular) for models for which direct estimation through maximum likelihood is difficult (for example, when the likelihood cannot be obtained in closed form). Besides being a novel contribution to the area of agent-based modelling, we demonstrate how the model can be used in a regulation setting, to quantify the effect of the introduction of new financial regulation.
Acknowledgements
I would like to start by offering my sincerest gratitude to my supervisor, Gareth Peters, who has consistently provided support in my efforts to familiarise myself with new concepts. If I am proud of the work presented in this thesis, it is in no small part due to the patience he has exhibited during our collaboration and his unique knowledge, as well as his constant belief in my abilities throughout.
I would also like to thank my second supervisor, Mark Harman, who is responsible for my first steps in academic research, and indeed, my first publication.
I would like to thank my family for their backing since the very first day of my undergraduate degree, and without them none of this would have been possible. I am truly grateful for their encouragement to pursue scientific endeavour.
Finally, I would like to dedicate this work to my fiance´e, whom I met just prior to embarking on this journey. Chryso has always been confident in my ability to see this thesis through, and her support has been invaluable in difficult times. For this, and everything else that you do, I am indebted to you.
Publications and presentations
Accepted journal papers
1. Efstathios Panayi and Gareth W Peters. Liquidity commonality does not imply liquidity resilience commonality: A functional characterisation for ultra-high frequency cross-sectional lob data. to appear, Quantitative Finance Special Issue on Big Data Analytics, 2015b
Published conference and workshop papers
1. Efstathios Panayi and Gareth Peters. Survival models for the duration of bid-ask spread deviations. In 2014 IEEE Conference on Computational Intelligence for Financial Engineering & Economics (CIFEr), pages 9–16. IEEE, 2014
2. Efstathios Panayi, Mark Harman, and Anne Wetherilt. Agent-based modelling of stock markets using existing order book data. In Multi-Agent-Based Simulation XIII, pages 101–114. Springer, 2013
Submitted journal papers and working papers
1. Efstathios Panayi and Gareth Peters. Stochastic simulation framework for the limit order book using liquidity motivated agents. in review, Journal of Financial Engineering, 2015a
2. Efstathios Panayi, Gareth W Peters, Jon Danielsson, and Jean-Pierre Zigrand. Market liquidity resilience. London School of Economics Working Paper Series, 2014
3. Gareth William Peters, Ariane Chapelle, and Efstathios Panayi. Opening discussion on banking sector risk exposures and vulnerabilities from virtual currencies: An operational risk perspective. in review, Journal of Operational Risk, 2014
Acknowledgements
7
Presentations
Systemic Risk Centre meeting, Coopers Hall, London . . . . . . . . . . . . Oct 2014 Forecasting Financial Markets Conference, Marseille, France . . . . . . . May 2014 Computational Intelligence for Financial Engineering & Economics, London Feb 2014 Computational and Financial Econometrics, Senate House, London . . . . . Dec 2013 Recent advances in Algorithmic and High Frequency Trading, UCL, London May 2013 Multi-Agent-Based Simulation XIII International Workshop, Valencia, Spain July 2012
Posters
Theory of Big Data, UCL, London . . . . . . . . . . . . . . . . . . . . . . Jan 2015
International visits
Institute of Statistical Mathematics, Tokyo, Japan . . . . . . . . . . . Jul-Aug 2013
Contents
1 Introduction
21
1.1 Electronic trading and the Limit Order Book . . . . . . . . . . . . . . . 22
1.2 Market liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3 High-frequency trading effects and regulation . . . . . . . . . . . . . . 25
1.4 Thesis contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4.1 Processing high-frequency trading activity and developing an
efficient LOB implementation . . . . . . . . . . . . . . . . . . 26
1.4.2 Modelling the resilience of LOB liquidity . . . . . . . . . . . . 28
1.4.3 Quantifying the commonality in liquidity and resilience . . . . . 30
1.4.4 Modelling trading activity in the LOB . . . . . . . . . . . . . . 31
1.5 Outline of thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 LOB construction and descriptive statistics
36
2.1 Dataset and available order types . . . . . . . . . . . . . . . . . . . . . 38
2.2 Manipulating ‘flat’ order files to obtain useful LOB data . . . . . . . . . 39
2.3 Building the LOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3 LOB and liquidity related work
47
3.1 Importance of liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1.1 Firms and cost of capital . . . . . . . . . . . . . . . . . . . . . 48
3.1.2 Liquidity providers . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.3 Asset managers . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1.4 Exchanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.1.5 Regulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 LOB liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
8
CONTENTS
9
3.2.1 Fluctuation of liquidity . . . . . . . . . . . . . . . . . . . . . . 53 3.2.2 Liquidity measures . . . . . . . . . . . . . . . . . . . . . . . . 53 3.3 Empirical analysis of liquidity . . . . . . . . . . . . . . . . . . . . . . 59 3.3.1 Temporal variation in liquidity . . . . . . . . . . . . . . . . . . 59 3.3.2 Commonality in liquidity . . . . . . . . . . . . . . . . . . . . . 60 3.3.3 Impact of trading mechanisms . . . . . . . . . . . . . . . . . . 62 3.3.4 Impact of regulatory and exchange decisions on liquidity . . . . 63 3.4 Financial market simulation models . . . . . . . . . . . . . . . . . . . 64 3.4.1 Agent design . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4.2 Market structure . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.4.3 Model aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.4.4 Methods for estimating ABM parameters . . . . . . . . . . . . 74
4 Liquidity and resilience of the LOB
80
4.1 Modelling intra-day liquidity resilience . . . . . . . . . . . . . . . . . . 81
4.2 Defining liquidity resilience . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.1 Examples of TED liquidity resilience measures . . . . . . . . . 84
4.3 Features of the LOB data and TED observations . . . . . . . . . . . . . 84
4.3.1 Intra-day variation in liquidity resilience . . . . . . . . . . . . . 85
4.3.2 Data considerations and assumptions . . . . . . . . . . . . . . . 87
4.4 Liquidity resilience model formulation . . . . . . . . . . . . . . . . . . 88
4.4.1 Survival analysis introduction . . . . . . . . . . . . . . . . . . 88
4.4.2 Survival model specification . . . . . . . . . . . . . . . . . . . 89
4.4.3 Classes of survival models . . . . . . . . . . . . . . . . . . . . 90
4.4.4 AFT model estimation . . . . . . . . . . . . . . . . . . . . . . 93
4.4.5 Model LOB Covariates . . . . . . . . . . . . . . . . . . . . . . 94
4.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.5.1 Explanatory power . . . . . . . . . . . . . . . . . . . . . . . . 97
4.5.2 Model selection . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.5.3 Interpretation of covariates . . . . . . . . . . . . . . . . . . . . 102
4.5.4 Forecasting liquidity resilience . . . . . . . . . . . . . . . . . . 105
4.5.5 Liquidity drought extremes . . . . . . . . . . . . . . . . . . . . 107
CONTENTS
10
4.5.6 Results for the XLM liquidity measure . . . . . . . . . . . . . . 110 4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.7 Additional figures and tables . . . . . . . . . . . . . . . . . . . . . . . 112
5 Liquidity and resilience commonality
119
5.1 Introduction to component analysis and dimensionality reduction . . . . 120
5.1.1 Principal Components Analysis . . . . . . . . . . . . . . . . . 120
5.1.2 Independent Components Analysis . . . . . . . . . . . . . . . . 123
5.1.3 ICA procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.1.4 ICA component selection . . . . . . . . . . . . . . . . . . . . . 125
5.1.5 Implications of using PCA and ICA for data coming from dif-
ferent distributions . . . . . . . . . . . . . . . . . . . . . . . . 125
5.1.6 PCA and ICA regression . . . . . . . . . . . . . . . . . . . . . 128
5.2 Liquidity commonality in a secondary market (Chi-X): PCA, ICA and
regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.2.1 Independent Component Analysis . . . . . . . . . . . . . . . . 133
5.3 Liquidity resilience for high frequency data . . . . . . . . . . . . . . . 136
5.3.1 Summarising resilience behaviour . . . . . . . . . . . . . . . . 137
5.4 Functional data analysis characterisations of massive LOB data sets . . 139
5.5 Functional data summaries: smoothed functional representations for
LRPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.5.1 Defining a basis system for functional data representation . . . . 140
5.6 Functional principal components analysis . . . . . . . . . . . . . . . . 143
5.7 Functional principal component regression for LRPs . . . . . . . . . . . 147
5.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6 Liquidity motivated agent-based model of the LOB
154
6.1 New perspective: Stochastic agent-based models for the LOB . . . . . . 155
6.1.1 Limit Order Book simulation framework . . . . . . . . . . . . . 155
6.1.2 Stochastic agent representation: liquidity providers and deman-
ders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.2 Simulation based likelihood calibration . . . . . . . . . . . . . . . . . . 163
6.2.1 Background on Indirect Inference . . . . . . . . . . . . . . . . 165
Book
Efstathios Panayi
A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London.
Department of Computing University College London
May 15, 2015
2
I, Efstathios Panayi, confirm that the work presented in this thesis is my own, except for the parts indicated in my statement of conjoint work. Where information has been derived from other sources, I confirm that this has been indicated in the thesis.
Abstract
The contribution of this body of work is in developing new methods for modelling interactions in modern financial markets and understanding the origins of pervasive features of trading data. The advent of electronic trading and the improvement in trading technology has brought about vast changes in individual trading behaviours, and thus in the overall dynamics of trading interactions. The increased sophistication of market venues has led to the diminishing of the role of specialists in making markets, a more direct interaction between trading parties and the emergence of the Limit Order Book (LOB) as the pre-eminent trading system. However, this has also been accompanied by an increased fluctuation in the liquidity available for immediate execution, as market makers try to balance the provision of liquidity against the probability of an adverse price move, with liquidity traders being increasingly aware of this and searching for the optimal placement strategy to reduce execution costs.
The varying intra-day liquidity levels in the LOB are one of the main issues examined here. The thesis proposes a new measure for the resilience of liquidity, based on the duration of intra-day liquidity droughts. The flexible survival regression framework employed can accommodate any liquidity measure and any threshold liquidity level of choice to model these durations, and relate them to covariates summarising the state of the LOB. Of these covariates, the frequency of the droughts and the value of the liquidity measure are found to have substantial power in explaining the variation in the new resilience metric. We have shown that the model also has substantial predictive power for the duration of these liquidity droughts, and could thus be of use in estimating the time between subsequent tranches of a large order in an optimal execution setting.
A number of recent studies have uncovered a commonality in liquidity that extends across markets and across countries. We outline the implications of using the PCA regression approaches that have been employed in recent studies through synthetic examples, and demonstrate that using such an approach for the study of Euro-
Abstract
4
pean stocks can mislead regarding the level of liquidity commonality. We also propose a method via which to measure commonality in liquidity resilience, using an extension of the resilience metric identified earlier. This involves the first use of functional data analysis in this setting, as a way of summarising resilience data, as well as measuring commonality via functional principal components analysis regression.
Trading interactions are considered using a form of agent-based modelling in the LOB, where the activity is assumed to arise from the interaction of liquidity providers, liquidity demanders and noise traders. The highly detailed nature of the model entails that one can quantify the dependence between order arrival rates at different prices, as well as market orders and cancellations. In this context, we demonstrate the value of indirect inference and simulation-based estimation methods (multi-objective optimisation in particular) for models for which direct estimation through maximum likelihood is difficult (for example, when the likelihood cannot be obtained in closed form). Besides being a novel contribution to the area of agent-based modelling, we demonstrate how the model can be used in a regulation setting, to quantify the effect of the introduction of new financial regulation.
Acknowledgements
I would like to start by offering my sincerest gratitude to my supervisor, Gareth Peters, who has consistently provided support in my efforts to familiarise myself with new concepts. If I am proud of the work presented in this thesis, it is in no small part due to the patience he has exhibited during our collaboration and his unique knowledge, as well as his constant belief in my abilities throughout.
I would also like to thank my second supervisor, Mark Harman, who is responsible for my first steps in academic research, and indeed, my first publication.
I would like to thank my family for their backing since the very first day of my undergraduate degree, and without them none of this would have been possible. I am truly grateful for their encouragement to pursue scientific endeavour.
Finally, I would like to dedicate this work to my fiance´e, whom I met just prior to embarking on this journey. Chryso has always been confident in my ability to see this thesis through, and her support has been invaluable in difficult times. For this, and everything else that you do, I am indebted to you.
Publications and presentations
Accepted journal papers
1. Efstathios Panayi and Gareth W Peters. Liquidity commonality does not imply liquidity resilience commonality: A functional characterisation for ultra-high frequency cross-sectional lob data. to appear, Quantitative Finance Special Issue on Big Data Analytics, 2015b
Published conference and workshop papers
1. Efstathios Panayi and Gareth Peters. Survival models for the duration of bid-ask spread deviations. In 2014 IEEE Conference on Computational Intelligence for Financial Engineering & Economics (CIFEr), pages 9–16. IEEE, 2014
2. Efstathios Panayi, Mark Harman, and Anne Wetherilt. Agent-based modelling of stock markets using existing order book data. In Multi-Agent-Based Simulation XIII, pages 101–114. Springer, 2013
Submitted journal papers and working papers
1. Efstathios Panayi and Gareth Peters. Stochastic simulation framework for the limit order book using liquidity motivated agents. in review, Journal of Financial Engineering, 2015a
2. Efstathios Panayi, Gareth W Peters, Jon Danielsson, and Jean-Pierre Zigrand. Market liquidity resilience. London School of Economics Working Paper Series, 2014
3. Gareth William Peters, Ariane Chapelle, and Efstathios Panayi. Opening discussion on banking sector risk exposures and vulnerabilities from virtual currencies: An operational risk perspective. in review, Journal of Operational Risk, 2014
Acknowledgements
7
Presentations
Systemic Risk Centre meeting, Coopers Hall, London . . . . . . . . . . . . Oct 2014 Forecasting Financial Markets Conference, Marseille, France . . . . . . . May 2014 Computational Intelligence for Financial Engineering & Economics, London Feb 2014 Computational and Financial Econometrics, Senate House, London . . . . . Dec 2013 Recent advances in Algorithmic and High Frequency Trading, UCL, London May 2013 Multi-Agent-Based Simulation XIII International Workshop, Valencia, Spain July 2012
Posters
Theory of Big Data, UCL, London . . . . . . . . . . . . . . . . . . . . . . Jan 2015
International visits
Institute of Statistical Mathematics, Tokyo, Japan . . . . . . . . . . . Jul-Aug 2013
Contents
1 Introduction
21
1.1 Electronic trading and the Limit Order Book . . . . . . . . . . . . . . . 22
1.2 Market liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3 High-frequency trading effects and regulation . . . . . . . . . . . . . . 25
1.4 Thesis contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4.1 Processing high-frequency trading activity and developing an
efficient LOB implementation . . . . . . . . . . . . . . . . . . 26
1.4.2 Modelling the resilience of LOB liquidity . . . . . . . . . . . . 28
1.4.3 Quantifying the commonality in liquidity and resilience . . . . . 30
1.4.4 Modelling trading activity in the LOB . . . . . . . . . . . . . . 31
1.5 Outline of thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 LOB construction and descriptive statistics
36
2.1 Dataset and available order types . . . . . . . . . . . . . . . . . . . . . 38
2.2 Manipulating ‘flat’ order files to obtain useful LOB data . . . . . . . . . 39
2.3 Building the LOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3 LOB and liquidity related work
47
3.1 Importance of liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1.1 Firms and cost of capital . . . . . . . . . . . . . . . . . . . . . 48
3.1.2 Liquidity providers . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.3 Asset managers . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1.4 Exchanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.1.5 Regulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 LOB liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
8
CONTENTS
9
3.2.1 Fluctuation of liquidity . . . . . . . . . . . . . . . . . . . . . . 53 3.2.2 Liquidity measures . . . . . . . . . . . . . . . . . . . . . . . . 53 3.3 Empirical analysis of liquidity . . . . . . . . . . . . . . . . . . . . . . 59 3.3.1 Temporal variation in liquidity . . . . . . . . . . . . . . . . . . 59 3.3.2 Commonality in liquidity . . . . . . . . . . . . . . . . . . . . . 60 3.3.3 Impact of trading mechanisms . . . . . . . . . . . . . . . . . . 62 3.3.4 Impact of regulatory and exchange decisions on liquidity . . . . 63 3.4 Financial market simulation models . . . . . . . . . . . . . . . . . . . 64 3.4.1 Agent design . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4.2 Market structure . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.4.3 Model aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.4.4 Methods for estimating ABM parameters . . . . . . . . . . . . 74
4 Liquidity and resilience of the LOB
80
4.1 Modelling intra-day liquidity resilience . . . . . . . . . . . . . . . . . . 81
4.2 Defining liquidity resilience . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.1 Examples of TED liquidity resilience measures . . . . . . . . . 84
4.3 Features of the LOB data and TED observations . . . . . . . . . . . . . 84
4.3.1 Intra-day variation in liquidity resilience . . . . . . . . . . . . . 85
4.3.2 Data considerations and assumptions . . . . . . . . . . . . . . . 87
4.4 Liquidity resilience model formulation . . . . . . . . . . . . . . . . . . 88
4.4.1 Survival analysis introduction . . . . . . . . . . . . . . . . . . 88
4.4.2 Survival model specification . . . . . . . . . . . . . . . . . . . 89
4.4.3 Classes of survival models . . . . . . . . . . . . . . . . . . . . 90
4.4.4 AFT model estimation . . . . . . . . . . . . . . . . . . . . . . 93
4.4.5 Model LOB Covariates . . . . . . . . . . . . . . . . . . . . . . 94
4.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.5.1 Explanatory power . . . . . . . . . . . . . . . . . . . . . . . . 97
4.5.2 Model selection . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.5.3 Interpretation of covariates . . . . . . . . . . . . . . . . . . . . 102
4.5.4 Forecasting liquidity resilience . . . . . . . . . . . . . . . . . . 105
4.5.5 Liquidity drought extremes . . . . . . . . . . . . . . . . . . . . 107
CONTENTS
10
4.5.6 Results for the XLM liquidity measure . . . . . . . . . . . . . . 110 4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.7 Additional figures and tables . . . . . . . . . . . . . . . . . . . . . . . 112
5 Liquidity and resilience commonality
119
5.1 Introduction to component analysis and dimensionality reduction . . . . 120
5.1.1 Principal Components Analysis . . . . . . . . . . . . . . . . . 120
5.1.2 Independent Components Analysis . . . . . . . . . . . . . . . . 123
5.1.3 ICA procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.1.4 ICA component selection . . . . . . . . . . . . . . . . . . . . . 125
5.1.5 Implications of using PCA and ICA for data coming from dif-
ferent distributions . . . . . . . . . . . . . . . . . . . . . . . . 125
5.1.6 PCA and ICA regression . . . . . . . . . . . . . . . . . . . . . 128
5.2 Liquidity commonality in a secondary market (Chi-X): PCA, ICA and
regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.2.1 Independent Component Analysis . . . . . . . . . . . . . . . . 133
5.3 Liquidity resilience for high frequency data . . . . . . . . . . . . . . . 136
5.3.1 Summarising resilience behaviour . . . . . . . . . . . . . . . . 137
5.4 Functional data analysis characterisations of massive LOB data sets . . 139
5.5 Functional data summaries: smoothed functional representations for
LRPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.5.1 Defining a basis system for functional data representation . . . . 140
5.6 Functional principal components analysis . . . . . . . . . . . . . . . . 143
5.7 Functional principal component regression for LRPs . . . . . . . . . . . 147
5.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6 Liquidity motivated agent-based model of the LOB
154
6.1 New perspective: Stochastic agent-based models for the LOB . . . . . . 155
6.1.1 Limit Order Book simulation framework . . . . . . . . . . . . . 155
6.1.2 Stochastic agent representation: liquidity providers and deman-
ders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.2 Simulation based likelihood calibration . . . . . . . . . . . . . . . . . . 163
6.2.1 Background on Indirect Inference . . . . . . . . . . . . . . . . 165