Stochastic Modelling of Big Data in Finance 9781032209265, 9781000776812, 9781032209289, 9781003265986

Stochastic Modelling of Big Data in Finance provides a rigorous overview and exploration of stochastic modelling of big

184 27 5MB

English Pages 280 Year 2023

Stochastic Modelling of Big Data in Finance
9781032209265, 9781000776812, 9781032209289, 9781003265986

Author / Uploaded
Anatoliy Swishchuk

Table of contents :
Foreword

Preface

Symbols

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

1.3.5 Modelling of LOB with a Non-linear General Compound Hawkes Processes

1.3.6 Modelling of LOB with a Multivariable General Compound Hawkes Processes

1.4 Illustration and Justification of Our Method to Study Big Data in Finance

1.4.1 Numerical Results: Lobster Data (Apple, Google and Microsoft Stocks)

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

1.6 Conclusion

Bibliography

I Semi-Markovian Modelling of Big Data in Finance

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: Pa(1,1)=Pa(−1,−1) and Pb(1,1)=Pb(−1,−1)

2.4.2 Other cases: either Pa(1,1)

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