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Stochastic modelling of big data in finance /

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Bibliographic Details
Main Author: Swishchuk, Anatoliy (Author)
Corporate Author: EBSCOhost
Format: eBook
Language:English
Published: Boca Raton, FL : CRC Press, 2023.
Series:Chapman and Hall/CRC financial mathematics series
Subjects:
Finance > Mathematical models.
Stochastic models.
Big data.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Half Title
  • Series Page
  • Title Page
  • Copyright Page
  • Dedication
  • 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) < Pa(-1, -1) or Pb(1, 1) < Pb(-1, -1)
  • 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 f and f
  • 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 for Generalizing the Model
  • 3.1.2. Data
  • 3.2. Reviewing the Assumptions with Our New Data Sets
  • 3.2.1. Liquidity of Our Data
  • 3.2.2. Empirical Distributions of Initial Queue Sizes and Calculated Conditional Probabilities
  • 3.2.3. Inter-arrival Times of Book Events
  • 3.2.4. Asymptotic Analysis