Stochastic Modelling of Big Data in Finance (Chapman and Hall/CRC Financial Mathematics Series)

Stochastic Modelling of Big Data in Finance provides a rigorous overview and exploration of sto- chastic 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 math- ematics 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 Dr. Anatoliy Swishchuk is a Professor in Mathematical Finance at the Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada. He got his B.Sc. and M.Sc. degrees from Kyiv State University, Kyiv, Ukraine. He earned two doctorate degrees in Mathematics and Physics (PhD and DSc) from the prestigious National Academy of Sciences of Ukraine (NASU), Kiev, Ukraine, and is a recipient of NASU award for young scientist with a gold medal for series of research publica- tions in random evolutions and their applications. Dr. Swishchuk is a chair and organizer of finance and energy finance seminar ‘Lunch at the Lab’ at the Department of Mathematics and Statistics. Dr. Swishchuk is a Director of Mathematical and Compu- tational Finance Laboratory at the University of Calgary. He was a steering committee member of the Professional Risk Managers International Association (PRMIA), Canada (2006-2015), and is a steer- ing committee member of Global Association of Risk Professionals (GARP), Canada (since 2015). Dr. Swishchuk is a creator of mathematical finance program at the Department of Mathematics & Sta- tistics. He is also a proponent for a new specialization “Financial and Energy Markets Data Modelling” in the Data Science and Analytics program. His research areas include financial mathematics, ran- dom evolutions and their applications, biomathematics, stochastic calculus, and he serves on editorial boards for four research journals. He is the author of more than 200 publications, including 15 books and more than 150 articles in peer-reviewed journals. In 2018 he received a Peak Scholar award. 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)