Stochastic modelling of big data in finance:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
2023
|
| Ausgabe: | First edition |
| Schriftenreihe: | Chapman and Hall/CRC financial mathematics
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| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034009942&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Abstract: | This book provides a rigorous overview and exploration of stochastic modelling of big data in finance (BDF). The book describes various stochastic models, including multivariate models, to deal with big data in finance. This includes data in high-frequency and algorithmic trading, specifically in limit order books (LOB) |
| Umfang: | xxiii, 280 Seiten Illustrationen, Diagramme |
| ISBN: | 9781032209265 |
Internformat
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| 490 | 0 | |a Chapman and Hall/CRC financial mathematics | |
| 520 | 3 | |a This book provides a rigorous overview and exploration of stochastic modelling of big data in finance (BDF). The book describes various stochastic models, including multivariate models, to deal with big data in finance. This includes data in high-frequency and algorithmic trading, specifically in limit order books (LOB) | |
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Datensatz im Suchindex
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Contents Foreword xiii Preface xv Symbols xxi Acknowledgements 1 A Brief Introduction: Stochastic Modelling of Big Data in Finance 1.1 Introduction . 1.2 Big Data in Finance: Limit Order Books . 1.2.1 Description of Limit Order Books Mechanism. 1.2.2 Big Data in Finance: Lobster Data. 1.2.3 More Big Data in Finance: Xetra and Frankfurt Markets (Deutsche Boerse Group), on September 23, 2013 and CISCO Data on November 3, 2014. 1.3 Stochastic Modelling of Big Data in Finance: Limit Order Books (LOB). 1.3.1 Semi-Markov Modelling of LOB . 1.3.2 General Semi-Markov Modelling of LOB. 1.3.3 Modelling of LOB with a Compound Hawkes Processes 1.3.4 Modelling of LOB with a General Compound Hawkes Processes. 11 1.3.5 Modelling of LOB with a Non-linear General Compound Hawkes Processes. 12 1.3.6 Modelling of LOB with a Multivariable General Compound Hawkes Processes. 12 1.4 Illustration and Justification of Our Method to Study Big Data in Finance . 12 1.4.1 Numerical Results: Lobster Data (Apple, Google and Microsoft Stocks). 13 1.4.2 Numerical Results: Xetra and Frankfurt Markets stocks (Deutsche Boerse
Group), on September 23, 2013 . 1.4.3 Numerical Results: CISCO Data, November 3, 2014 . 1.5 Methodological Aspects of Using the Models . xxiii 1 1 3 3 4 5 6 7 9 10 14 15 15 vii
viii Contents 1.6 Conclusion . Bibliography. I g Semi-Markovian Modelling of Big Data in Finance 21 2 A Semi-Markovian Modelling of Big Data in Finance 2.1 Introduction . 2.2 A Semi-Markovian Modelling of Limit Order Markets . 2.2.1 Markov Renewal and Semi-Markov Processes. 2.2.2 Semi-Markovian Modelling of Limit Order Books . 2.3 Main Probabilistic Results . 2.3.1 Duration until the next price change. 2.3.2 Probability of Price Increase . 2.3.3 The stock price seen as a functional of a Markov renewal process. 2.4 Diffusion Limit of the Price Process . 2.4.1 Balanced Order Flow case: P“(l, 1) = Pa(—1, —1) and P₺(l,l) = Pb(-1,-1). 2.4.2 Other cases: either P°(l,l) Pa(—1,—1) or Pb(l,l) Pb(֊l,-l). 2.5 Numerical Results. 2.6 More Big Data. 2.6.1 More
Data. 2.6.2 Estimated Probabilities. 2.6.3 Assumption on Distributions ƒ andƒ . 2.6.4 Diffusion Limit (Not-Fixed Spread). 2.6.5 The Optimal Liquidation/Acquisition Problems . 2.6.6 Market Making. 2.7 Conclusion . Bibliography. 3 General Semi-Markovian Modelling of Big Data in Finance 3.1 Introduction . 3.1.1 Motivation forGeneralizing the Model. 3.1.2 Data. 3.2 Reviewing the Assumptions with OurNew Data Sets . 3.2.1 Liquidity of Our Data. 3.2.2 Empirical Distributions of Initial Queue Sizes and Calculated ConditionalProbabilities. 3.2.3 Inter-arrival Times of Book Events. 3.2.4 Asymptotic Analysis. 3.3 General Semi-Markov Model for the Limit Order Book with Two States . 72 3.3.1 Diffusion Limits . 23 26 26 27 32 32 38
38 40 41 44 45 51 51 54 59 60 61 62 62 63 67 67 68 69 69 69 70 71 72 73
Contents Implementation. Numerical Results. Application of the Model . 3.3.4.1 Examination of the Data. 3.3.4.2 Model Implementation . 3.3.4.3 Results for Constructed Sample Day. 3.4 General Semi-Markov Model for the Limit Order Book with arbitrary number of states . 85 3.4.1 Justification. 3.4.2 Diffusion Limits . 3.4.3 Implementation. 3.4.4 Numerical Results. 3.5 Discussion on Price Spreads . 3.6 Conclusion . Bibliography . 85 86 89 90 91 94 94 Modelling of Big Data in Finance with Hawkes Processes 97 3.3.2 3.3.3 3.3.4 II 4 ix 77 78 79 80 82 83 A Brief Introduction to Hawkes Processes 99 4.1 Introduction . 99 4.2 Definition of Hawkes Processes(HPs) . 101 4.3 Compound Hawkes
Processes. 104 4.3.1 Special Cases of Compound Hawkes Processes in Limit Order Books. 105 4.4 Limit Theorems for Hawkes Processes: LLN and FCLT . . . 106 4.4.1 Law of Large Numbers (LLN) for Hawkes Processes . 106 4.4.2 Functional Central Limit Theorems (FCLT) for Hawkes Processes. 107 4.5 Limit Theorems for Poisson Processes: LLN and FCLT . . . 107 4.5.1 Law of Large Numbers (LLN) for Poisson Processes . 107 4.5.2 Functional Central Limit Theorems (FCLT) for Hawkes Processes. 107 4.6 Stylized Properties of Hawkes Process. 107 4.6.1 Non-exponential Inter-arrival Times. 108 4.6.2 Clustering Effect of Trades. 110 4.6.3 Non-independency of Mid-priceChanges. 112 4.7 Conclusion . 115 Bibliography . 115 5 Stochastic Modelling of Big Data in Finance with CHP 5.1 Introduction . 5.2 Definitions of HP, CHP and RSCHP. 5.2.1 One-dimensional Hawkes Process. 5.2.2 Compound Hawkes Process (CHP). 121 121
123 123 125
Contents 5.2.3 Regime-switching Compound Hawkes Process. Diffusion Limits and LLNs for CHP and RSCHP in Limit Order Books. ^^ 5.3.1 Diffusion Limits for CHP in Limit Order Books . 5.3.2 LLN for CHP. 5.3.3 Corollary: Extension to a Point Process. 5.3.4 Diffusion Limits for RSCHP in Limit Order Books . . 5.3.5 LLN for RSCHP. 5.4 Numerical Examples and Parameters Estimations . 5.4.1 Parameters Estimation for CISCO Data. 5.4.2 Error of Estimation . 5.4.3 Graphs based on Parameters Estimation for CISCO Data (5 Days, 3-7 November 2014 ([Cartea et al., 2015])) from Section 4.1 . 5.4.4 Remark on Regime-switching Case (Section 3.4) . . . 5.5 Conclusion . Bibliography. 126 5.3 127 129 130 131 133 134 134 136 137 140 140 140 6 Stochastic Modelling of Big Data in Finance with GCHP 145 6.1 A Brief Introduction andLiterature Review. 145 6.2 Diffusion Limits and LLNs . 147 6.2.1 Diffusion Limit and LLN forNLCHPnSDO. 147
6.2.2 Diffusion Limit and LLN forGCHPnSDO. 150 6.2.3 Diffusion Limits and LLNsforSpecial Cases of GCHPnSDO. 152 6.3 Empirical Results . 154 6.3.1 CHPDO. 155 6.3.2 GCHP2SDO. 157 6.3.3 GCHPNSDO. 158 6.3.4 Quantitative Analysis. Ιθθ 6.3.5 Remarks. Ιθΐ 6.3.6 Figures to Chapter 6. Ig2 6.4 Conclusion . 169 Bibliography.՜ 16g 7 Quantitative and Comparative Analyses of Big Data with GCHP 173 7.1 Introduction . 173 7.2 Theoretical Analysis. 176 7.2.1 One-dimensional Hawkes Process 176 7.2.1.1 Definition. 176 7.2.1.2 Calibration. 176 7.2.2 General Compound Hawkes Process. л 177 7.2.2.1 Definition. 177 7.2.2.2 Diffusive Limit 177
Contents Application. 7.3.1 Limit Order Book. 7.3.2 Data. 7.3.3 Descriptive Data Analysis. 7.3.3.1 QQ-plot. 7.3.3.2 Autocorrelation . 7.3.3.3 Clustering Feature. 7.4 Hawkes Process and Models Calibrations . 7.4.1 Hawkes Process’ ParametersCalibration. 7.4.2 Mid Price Modelling and Calibration. 7.4.2.1 GCHPDO . 7.4.2.2 GCHP2SDO. 7.4.2.3 GCHPnSDO. 7.5 Error Measurement . 7.6 Conclusion . Bibliography . 7.3 III xi 178 178 179 179 179 183 185 185 187 187 188 190 191 194 199 199 Multivariate Modelling of Big Data in Finance 201 8 Multivariate General Compound Hawkes Processes in BDF 203 Introduction . Hawkes Processes and Limit Theorems
. 8.2.1 One-dimensional Hawkes Process. 8.2.2 Multivariate Hawkes Process (МНР) and Limit Theorems. 206 8.3 Multivariate General Compound Hawkes Processes (MGCHP) and Limit Theorems. 207 8.4 FCLT II for MGCHP: DeterministicCentralization . 8.5 Numerical Example . 8.5.1 Data Description. 8.5.2 Maximum Likelihood Estimation (MLE). 8.5.3 Calibration and Empirical Analysis by FCLT I for MGCHP with Stochastic Centralization. 8.5.4 Empirical Analysis by FCLT II for MGCHP with Deterministic Centralization. 217 8.6 Conclusion . Bibliography . 8.1 8.2 9 Multivariate General Compound Point Processes in BDF 9.1 Introduction . 9.2 Definition of Multivariate General Compound Point Process (MGCPP) . 225 9.2.1 Assumptions for MultivariatePoint Processes. 9.2.2 Definition for MGCPP. 9.3 LLNs and Diffusion Limits for MGCPP
. 203 204 204 211 213 213 213 215 219 219 223 223 225 226 227
Contents xii LLN for MGCPP. Diffusion Limits for MGCPP: Stochastic Centralization Numerical Examples for FCLT: Stochastic Centralization. 9.3.3.1 Data Description and Parameter Estimations 9.3.3.2 Comparison with MGCHP with Two Dependent Orders. 9.3.3.3 MGCPP with ^State Dependent Orders . . 9.4 Diffusion Limit for the MGCPP: Deterministic Centralization 9.4.1 FCLT for MGCPP: Deterministic Centralization . . . 9.4.2 Numerical Examples for FCLT: Deterministic Centralization . . 241 9.4.3 Rolling Cross-Validation. 9.5 Conclusion . Bibliography. 9.3.1 9.3.2 9.3.3 IV Appendix: Basics in StochasticProcesses 227 228 շ31 231 233 236 239 239 242 245 245 249 A Basics in Stochastic Processes 251 A.l Discrete-time Markov Chains . 251 A.1.1 Continuous-time Markov Chains. 253 A. 1.2 Ergodicity and Reducibility of MarkovChains . 256 A.2 Markov Renewal Processes . 262 A.3 Semi-Markov Processes . 264 A.4 Jump Markov
Processes. 267 A.5 Wiener Processes and DiffusionProcesses. 268 A.6 Counting and Poisson Process . 269 A.6.1 Counting Process (CP) . 269 A.6.2 Poisson Process (PP) . 270 A.6.3 Compound Poisson Process (CPP). 270 A.7 Hawkes Processes . 271 A.8 Martingales. 273 A.9 Martingale Characterization of Markov and Semi-Markov Processes. 274 A.9.1 Martingale Characterization of Markov Chains 274 A.9.2 Martingale Characterization of Markov Processes 275 A.9.3 Martingale Characterization of Semi-Markov Processes 276 A. 10 Conclusion . շ?? Bibliography. . Index 279 |
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| id | DE-604.BV048634947 |
| illustrated | Illustrated |
| indexdate | 2025-01-11T15:18:38Z |
| institution | BVB |
| isbn | 9781032209265 |
| language | English |
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| spelling | Sviščuk, Anatolij Verfasser (DE-588)1048087905 aut Stochastic modelling of big data in finance Anatoliy Swishchuk First edition Boca Raton ; London ; New York CRC Press, Taylor & Francis Group 2023 xxiii, 280 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Chapman and Hall/CRC financial mathematics This book provides a rigorous overview and exploration of stochastic modelling of big data in finance (BDF). The book describes various stochastic models, including multivariate models, to deal with big data in finance. This includes data in high-frequency and algorithmic trading, specifically in limit order books (LOB) Wirtschaft (DE-588)4066399-1 gnd rswk-swf Big Data (DE-588)4802620-7 gnd rswk-swf Finanzmanagement (DE-588)4139075-1 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 s Big Data (DE-588)4802620-7 s Wirtschaft (DE-588)4066399-1 s Finanzmanagement (DE-588)4139075-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-003-26598-6 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034009942&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sviščuk, Anatolij Stochastic modelling of big data in finance Wirtschaft (DE-588)4066399-1 gnd Big Data (DE-588)4802620-7 gnd Finanzmanagement (DE-588)4139075-1 gnd Statistisches Modell (DE-588)4121722-6 gnd |
| subject_GND | (DE-588)4066399-1 (DE-588)4802620-7 (DE-588)4139075-1 (DE-588)4121722-6 |
| title | Stochastic modelling of big data in finance |
| title_auth | Stochastic modelling of big data in finance |
| title_exact_search | Stochastic modelling of big data in finance |
| title_full | Stochastic modelling of big data in finance Anatoliy Swishchuk |
| title_fullStr | Stochastic modelling of big data in finance Anatoliy Swishchuk |
| title_full_unstemmed | Stochastic modelling of big data in finance Anatoliy Swishchuk |
| title_short | Stochastic modelling of big data in finance |
| title_sort | stochastic modelling of big data in finance |
| topic | Wirtschaft (DE-588)4066399-1 gnd Big Data (DE-588)4802620-7 gnd Finanzmanagement (DE-588)4139075-1 gnd Statistisches Modell (DE-588)4121722-6 gnd |
| topic_facet | Wirtschaft Big Data Finanzmanagement Statistisches Modell |
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