Stochastic modelling of big data in finance [electronic resource]

• 作者： Swishchuk, Anatoliy, author.
• 出版： Boca Raton, FL : CRC Press
• 叢書名： Chapman and Hall/CRC financial mathematics series
• 主題： Finance--Mathematical models. , Stochastic models. , Big data. , Finances--Modeles mathematiques. , Modeles stochastiques. , Donnees volumineuses. , Big data , Finance--Mathematical models , Stochastic models
• ISBN： 9781000776805 (electronic bk.) 、 1000776808 (electronic bk.)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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 3.3. General Semi-Markov Model for the Limit Order Book with Two States
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• 摘要註: "Stochastic Modelling of Big Data in Finance 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), and shows how those models can be applied to different datasets to describe the dynamics of LOB, and to figure out which model is the best with respect to a specific data set. The results of the book may be used to also solve acquisition, liquidation and market making problems, and other optimization problems in finance. Features Self-contained book suitable for graduate students and post-doctoral fellows in financial mathematics and data science, as well as for practitioners working in the financial industry who deal with big data All results are presented visually to aid in understanding of concepts"--
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