Short‐Term Stock Price Prediction Based on Limit Order Book Dynamics

• Date: 01 August 2017
• Published date: 01 August 2017
• Author: Yang An,Ngai Hang Chan
• DOI: http://doi.org/10.1002/for.2452

Journal of Forecasting,J. Forecast. 36, 541–556 (2017)

Published online 23 November 2016 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/for.2452

Short-Term Stock Price Prediction Based on Limit Order

Book Dynamics

YAN G AN 1AND NGAI HANG CHAN2

1

Credit Suisse, One Cabot Square, London, UK

2

Southwestern University of Finance and Economics and The Chinese University of Hong Kong,

Hong Kong

ABSTRACT

Interaction of capital market participants is a complicated dynamic process. A stochastic model is proposed to describe

the dynamics to predict short-term stock price behaviors. Independent compound Poisson processes are introduced to

describe the occurrences of market orders, limit orders and cancellations of limit orders, respectively. Based on high-

frequency observations of the limit order book, the maximum empirical likelihood estimator (MELE) is applied to

estimate the parameters of the compound Poisson processes. Moreover,an analytical formula is derived to compute the

probability distribution of the first-passage time of a compound Poisson process. Based on this formula, the conditional

probability of a price increase and the conditional distribution of the duration until the first change in mid-price are

obtained. A novel approach of short-term stock price prediction is proposed and this methodology works reasonably

well in the data analysis. Copyright © 2016 John Wiley & Sons, Ltd.

KEY WORDS compound Poisson processes; first passage time; limit order book; maximum empirical

likelihood estimator; stock price prediction

INTRODUCTION

Studies of financial trading have initially concentrated on quote-driven markets, where traders transact with deal-

ers (market makers) who post bid and ask prices and provide liquidity. In recent years, developments of electronic

communications networks (ECNs) have provided an alternative order-driven trading system, where traders directly

transact with other traders and there is no intermediary dealer. These electronic platforms gather all outstanding limit

orders into a limit order book, which is available to all market participants.

The order-driven trading system may involve more competition and result in better prices, but it also has more

complexity. Unlikein a quote-driven market, where modeling the behaviors of a few market makers is sufficient, there

are thousands of anonymous traders in an order-driven market. These traders arrive randomly, choose whether they

want to execute immediately,determine how large their order sizes should be, and even cancel their orders at any time

to exit the market strategically. Despite its complexity, models of order book dynamics are of great interest not only

because they can be applied to optimize trade execution strategies (Alfonsi et al., 2010; Obizhaeva and Wang, 2006;

Predoiu et al., 2011; Guilbaud and Pham, 2013; Goettler et al., 2005, 2009), but also because these models provide

insight into the relationship between supply and demand (Farmer et al., 2004; Foucault et al., 2005). Empirical studies

indicate that the formation of short-term price behavior depends on the evolution of limit order books (Parlour, 1998;

Harris and Panchapagesan, 2005; Rosu, 2009).

Statistical features of limit order book dynamics are investigated in various empirical studies (Bouchaud et al.,

2002; Hollifield et al., 2004; Smith et al., 2003; Gourieroux et al., 1999), but it remains a challenging task to capture

essential features into a single model. Cont and de Larrard (2011) propose a Markovian model of a limit order mar-

ket, which captures certain main features of market orders and limit orders and their influence on price dynamics, but

they only focus on the best bid and ask queues rather than the dynamics of the entire limit order book. Bouchaud et al.

(2008), Bovier et al. (2006), Luckock (2003) and Maslov and Mills (2001) propose stochastic models of order books,

but concentrate only on unconditional/steady-state distributions of various quantities. In this paper, probabilities con-

ditional on the current state of the limit order book are investigated instead. Cont et al. (2010) propose a model that

tracks the number of limit orders at each price level in the limit order book. These limit orders wait in a queue to be

executed against market orders or to be canceled. They assume that the occurrences of market events—incominglimit

orders, incoming market orders and cancellations of limit orders—follow independent Poisson processes. The inten-

sity parameter in each process models the occurrence frequency of market events and the size of each eventis assumed

to be unit. Although the formulation of the model leads to an analytically tractable framework where parameters can

Correspondence to: Ngai Hang Chan, Department of Statistics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong. E-mail:

nhchan@sta.cuhk.edu.hk

Copyright © 2016 John Wiley & Sons, Ltd

542 Y. An and N. H. Chan

be estimated and various conditional probabilities may be computed through Laplace transforms, they point out that

heterogeneity of order sizes and correlation of order flows need to be incorporated for future exploration. Zhao (2010)

and Toke (2011) extend Cont et al.’s (2010) model via considering the interdependence of market event arrival rates.

However, models of random order sizes are still lacking.

In this paper, a new stochastic model is proposed that describes the limit order book dynamics, where the order

flows are governed by independent compound Poisson processes. This model considers both the arrival frequency

of each order and the heterogeneity of order sizes, which is more realistic and reflects the complexities in the afore-

mentioned order-driven market. The model also enables a wide range of pricing quantities to be computed and the

dynamic shape of a limit order book to be predicted.

Likewise, stock price forecasting is a widely studied topic in various fields. There are traditionally two main

techniques to analyze stocks: fundamental analysis and technical analysis. Fundamental analysts attempt to study both

macroeconomic factors and company-specific factors with the goal of producing a fundamental value that investors

can compare with the current stock price. It is clear that fundamental analysis alone works well in the long term,

but it may not provide sufficient basis for short-term trading. Analysis of intrinsic value is one thing, but trading

relies on the behaviors of all market participants, and fundamental analysis has little concern about this. The other

approach is technical analysis, which analyzes stock price trends based on past market data—primarily price and

volume (Caginalp and Laurent, 1998; Brock et al., 1992). Techniques in artificial intelligence such as evolutionary

algorithms and artificial neural networks have subsequently been used to develop advanced models for stock price

prediction (Leigh et al., 2002; Larsen, 2010). A model of stock price evolution directly based on buying and selling

pressure is still missing, however. One of the important consequences of this paper is that a novel methodology of

price prediction based on supply/demand information from the limit order book is proposed. In this approach, short-

term stock price trends are predicted based on the interactions of buyers and sellers, which are reflected in the limit

order book dynamics. The data analysis shows that this method works reasonably well.

This paper is organized as follows. Section Models of limit order books introduces a model for limit order

book dynamics, where the occurrences of market events are described by independent compound Poisson processes.

Section Parameter estimation describes the maximum empirical likelihood estimator (MELE) for estimation of model

parameters from high-frequency limit order book time series data. This methodology is illustrated via a simulation

study. Various quantities regarding stock price behaviors are calculated in Section First passage time, followed by

simulation studies to demonstrate the accuracy of the theorems presented. Section An example reports the results of

an application of the model to the order book data and Section Discussion concludes.

MODELS OF LIMIT ORDER BOOKS

Limit order books

In an order-driven electronic platform, traders post two types of orders. A limit order is an order to trade at a price

level better than or equal to the limit price. In the case when market prices do not move to the limit, the trade will

not be executed, so it has execution uncertainty.Amarket order is an order to complete the trade immediately at

the best possible price. The emphasis in a market order is the speed of execution, but there is price uncertainty.All

outstanding limit orders are aggregated in a limit order book that is available to market participants. A limit order

stays in the order book until it is either executed against a market order or it is canceled, when the quantities available

in the limit order book are updated accordingly.

In this work, limit orders are placed on a price grid ¹n1;:::;n

2º, which denotes multiples of a price tick. Since

2001, the minimum tick size for stock trading above 1 dollar is 0.01. The range between n1and n2is selected to be

large enough such that it is highly unlikely for the stock price under consideration to fluctuate outside the range within

the time frame concerned. Since we focus on short-term stock price prediction in this thesis, the model is intended

to be used in the timescale of minutes and thus this finite price assumption is reasonable. The state of the limit order

book is tracked by a continuous process X.t/ D.X1.t /; : : : ; Xn.t//t0,wherenDn2n1C1and jXl.t /jis the

amount of outstanding limit orders at price pDlCn11; 1 ln. If the outstanding orders at the lth entry are

buy orders, then Xl.t/ is negative; otherwise, Xl.t / is positive.

The location of the ask price lA.t/ at time tis defined by

lA.t/ Dinf¹lD1;:::;n;X

l.t/ > 0º^.n C1/

and the corresponding ask price pA.t/ DlA.t / Cn11. Similarly, the location of the bid price lB.t/ at time tis

defined by

Copyright © 2016 John Wiley & Sons, Ltd J. Forecast. 36, 541–556 (2017)