Stochastic Modelling of Big Data in Finance
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Stochastic Modelling of Big Data in Finance Anatoliy Swishchuk1 Received: 19 April 2018 / Revised: 12 May 2020 / Accepted: 28 September 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We present a new approach to study big data in finance (specifically, in limit order books), based on stochastic modelling of price changes associated with high-frequency and algorithmic trading. We introduce a big data in finance, namely, limit order books (LOB), and describes them by Lobster data-academic data for studying LOB. Numerical results, associated with Lobster and other data, are presented, and explanation and justification of our method of studying of big data in finance are considered. We also describe various stochastic models for mid-price changes in the market, and explain how to use these models in practice, highlighting the methodological aspects of using the models. Keywords Big data in finance · Stochastic modelling · Limit order books · Semi-Markov modelling · Compound Hawkes pocess · General compound Hawkes process · Non-linear general compound Hawkes process · Multivariate general compound Hawkes process · LOBster data · CISCO data · Deutsche Boerse Group data · Methodological aspects of using the models Mathematics Subject Classification (2010) 60G55 · 60K15 · 91B50 · 91B70 · 60F05
1 Introduction Finance may be defined as the study of how people allocate scarce resources over time. The outcomes of financial decisions (costs and benefits) are usually spread over time and not known with certainty ahead of time, i.e subject to an element of risk. Decision makers must therefore be able to compare the values of cash-flows at different dates take a probabilistic/stochastic view. Big data has now become a driver of model building and analysis in a number of areas, including finance. More than half of the markets in today’s highly competitive
Research is supported by NSERC Anatoliy Swishchuk
[email protected] 1
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada
Methodology and Computing in Applied Probability
and relentlessly fast-paced financial world now use a limit order book (LOB) mechanism to facilitate trade. Two types of trading in equities are widely practiced today: high-frequency (limit-order and market) trading and statistical arbitrage or market neutral (generalized) pairs trading These types of trading account for well over two thirds the volume traded today. Main problem here is: how to deal with big data arising in electronic markets for algorithmic and high-frequency (milliseconds) trading that contain two types of orders, limit orders and market orders. It is not yet clear how to quantify the systemic risk, or the market instabilities generated by these types of trading. Systemic risk, or instabilities, occur in many complex systems: In ecology (diversity of species), in climate change, in material behaviour (phase transitions), insurance, finance, etc. Thus, of the areas of mathema
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