The effect of limit order flows at the best quotes on price changes

Abstract

We test the effect of order book events at the best quotes on price changes under the model proposed by Cont et al., in: Journal of Financial Econometrics 12 (2014), 47–88. The OFI (Order Flow Imbalance) measure in the model explains the price change of the nearby month KOSPI 200 futures contract reasonably well, which is one of the most liquidly traded securities in the world. The model becomes less accurate when the sampling time interval is shorter; the $R^{2}$ of the model drops to 40% for the time interval of 1 second, while it is around 70% when the time interval is longer than 1 minute. We postulate that this is related to the lead–lag effect between the OFI measure and the price change for shorter time intervals. We use the vector auto-regressive model to verify this conjecture.

Keywords

Granger causality KRDS (Korea Research Data Services)order flow imbalance limit order book event price impact

1. Introduction

The growing importance of limit orders in financial markets needs better understanding of the limit order book (LOB) dynamics.1

¹
We cite Parlour and Seppi [29]: “Now in 2007 most equity and derivative exchanges around the world are either pure electronic limit order markets or at least allow for customer limit orders in addition to an on-exchange market making”. See also [23] and [33].

A limit order book contains information on the supply and the demand, so it is natural to expect that order book events have a causality relationship with price changes. As buy (sell) orders accumulate near the best bid (ask) quote of the book, traders tend to submit more aggressive buy (sell) limit orders and market orders. This drives the price up (down). Biais et al. [1], Kaniel and Liu [24] and Cao et al. [4] show that the price revision moves in the direction of the previous limit order flow. On the other hand, information asymmetry exposes traders to the risk of being picked off by a superior trader with more accurate information (Copeland and Galai [8]). If a majority of traders revises their orders to control the picking-off risk (or free-option risk as in [11]), limit order flows affect the price change in the opposite direction, as explained in [5,18] and [6].

Cont et al. [7], Hautsch and Huang [21] and Eisler et al. [9] study predictability of returns from order book events. The most parsimonious model among those is the one proposed in [7], the CKS model hereafter. It defines the order flow imbalance (OFI) measure simply by market orders and limit orders observed at the best quotes, and draws a linear relationship between price changes and the OFI measure. Hautsch and Huang [21] propose a cointegrated vector autoregressive (VAR) model for quotes and the order book depth and estimates impulse response functions. Eisler et al. [9] propose a linear superposition model of the impact of past trades borrowing the idea from Bouchaud et al. [2].

We choose the CKS model to study the price impact of order book events. We test the model using the KOSPI 200 index futures market data. The market is liquid for nearby month contracts, but illiquid for other contracts. Our empirical result shows that the OFI measure of the CKS model explains the price change of the nearby month contract quite well. The $R^{2}$ of the linear regression is around 70% when the time interval is longer than 1 minute. This means that the accumulation of bid (ask) orders at the best bid (ask) quotes is linearly related to the rise (decline) of the mid price, since the OFI measure is defined as the imbalance between the supply and the demand at the best bid and the best ask. In contrast, it dose not work well for the second nearby month contract with this model.

For nearby month contracts, we observe that the linear relation between the OFI measure and the price change gets weaker when a sampling time interval becomes shorter. The $R^{2}$ of the linear regression declines to 40% when the interval is reduced to one second. One possible explanation of this phenomena is a short term effect of liquidity shocks. Gaps in the order book make abrupt changes.

Another explanation of the low accuracy of the model is the lead–lag effect between the OFI measure and the price change for a shorter time interval. As discussed above, traders revise or cancel their orders by observing the current status of the order book. This process needs a minimum time interval to reach a stable status. Therefore, the OFI measure cannot explain the price change enough for shorter intervals. We test the hypothesis by a vector regression analysis as in [19].2

Brown et al. [3] use a VAR model in the Australian Stock Exchange to find bi-directional causality between order imbalance and stock price return. Hautsch and Huang [21] use a cointegrated VAR model to test the case in Euronext Amsterdam. Wuyts [35] simulates a VAR model to test resiliency of aggressive orders in an order-driven market.

Empirical findings in this paper suggest that a price impact model of order book events such as [7] needs an extension that accommodates the dynamic of the order book.3

The general theoretical works on modeling a dynamic equilibrium in an order book market include Parlour [28], Foucault [13], Foucault et al. [14], Goettler et al. [15,16], etc. Parlour and Seppi [29] is an excellent review of this issue. For empirical evidence on the importance of dynamic order book structure, one may refer to [27] and references therein.

An empirical test shows that the CKS model is too simple to explain the complexity in the real world. Indeed, Cont et al. [7] intend to apply the OFI based model to the high frequency world. However, we show that it is not accurate when the time interval is very short, e.g., a second. As in [9], the assumption of the high liquidity is indispensable in [7]. In a limit order market, when the bid-ask spreads and the gaps between quoted prices are larger than the minimum tick size, there are a variety of ways by which price respond s to order book events.4

⁴

Eisler et al. [9] use the term ‘a small (large) tick stock’ to refer a liquid (illiquid) stock.

The remainder of the paper is organized as follows. We first review the CKS model in Section 2.1. In Section 2.2, we describe the data we use in this paper. Section 2.3 reports the empirical result obtained by fitting the CKS model and testing the linear relation between the OFI measure and the price change. From these, we conduct the vector auto-regression to find the existence of the lead–lag effect in Section 3. We also estimate the multiple linear regression considering the lead–lag effect. We conclude in Section 4.

2. Testing the CKS model in the KOSPI 200 futures market

2.1. The CKS model

In this section, we briefly summarize the price impact model proposed in [7].

Let us consider a time interval $[t - dt, t]$ which belongs to a longer time interval $[T_{i - 1}, T_{i}]$ . $dt$ represents a short time. Separation of longer time intervals is due to diurnal patterns in the high-frequency trading. For this issue, we refer to Jain and Joh [22], Mclnish and Wood [26], Foster and Viswanathan [12], etc. We estimate parameters in $[T_{i - 1}, T_{i}]$ . Let $L_{t}^{b}$ be the total size of buy orders that are submitted to the current best bid during the time interval. Similarly, let $C_{t}^{b}$ be the total size of buy orders that are cancelled from the current best bid during that time interval. $M_{t}^{b}$ denotes the total size of marketable buy orders. The quantities $L_{t}^{s}$ , $C_{t}^{s}$ and $M_{t}^{s}$ for sale orders are defined analogously. $P_{t}^{b}$ and $P_{t}^{a}$ denote the bid price and the ask price at time t, respectively.

Fig. 1.

The worldwide rankings of the KOSPI 200 index futures market. As of 2011, it is ranked the sixth by the number of contracts traded among the equity index futures markets in the world. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/RDA-150113.)

The order flow imbalance measure for each t is defined as follows: $\begin{matrix} (1) & {OFI}_{t} = L_{t}^{b} - C_{t}^{b} - M_{t}^{s} - L_{t}^{s} + C_{t}^{s} + M_{t}^{b} . \end{matrix}$ We consider the normalized mid price $\begin{matrix} P_{t} = \frac{P_{t}^{b} + P_{t}^{a}}{2 δ}, \end{matrix}$ where δ denotes the tick size. We assume that an order book can be approximated locally by uniform distributions. In other word, the number of shares (depth) at each price level beyond the best and ask is constant. Let us denote this value on the time interval $[T_{i - 1}, T_{i}]$ by $D_{i}$ . We also assume that order arrivals and cancelations occur only at the best bid and the best ask. Moreover, when the bid (or ask) size reaches $D_{i}$ , the next passive order arrives at a tick above (or below) the best quote, initializing the new best level. Then, we expect the following linear relationship between price changes and the OFI on each interval $[t_{k - 1, i}, t_{k, i}] \subset [T_{i - 1}, T_{i}]$ : $\begin{matrix} (2) & Δ P_{k, i} = β_{i} {OFI}_{k, i} + ϵ_{k, i}, \end{matrix}$ where $Δ P_{k, i} = P_{k, i} - P_{k, i - 1}$ , and $ϵ_{k, i}$ is a measurement error. $β_{i}$ is a price impact coefficient for an ith time interval, which changes with index i. Cont et al. [7] interpreted $\frac{1}{2 β_{i}}$ as an implied estimation of the order book depth $D_{i}$ .5

⁵

Cont et al. [7] claim that the price impact coefficient is a better estimate of Kyle’s λ than traditional estimates based on trade data. This is obviously not the case, for Kyle [25] considered an informed trader who uses market orders to utilize private information to generate profits. Since the OFI measure involves limit orders by a trader regardless of informativeness, we cannot compare two price impact coefficients directly.

2.2. Dataset

The KOSPI 200 index futures market is a purely order-driven market where the liquidity and prices are formed by traders through open competition. Since it opened in 1996, it has been one of the most liquid markets. As of 2011, it is ranked the sixth by the number of contracts traded among equity index futures markets in the world (Fig. 1).

Table 1
Summary of the trades and orders, the daily average

	Nearby month	The second nearby month
Number of sell market order (amount)	37,673.028 (152,426.600)	315.542 (881.261)
Number of buy market order (amount)	36,720.571 (151,389.400)	299.498 (863.398)
Number of buy limit order (amount)	158,315.623 (435,674.600)	22,168.028 (187,481.900)
At the best bid	61,859.615 (202,088.600)	8955.847 (62,039.200)
Number of sell limit order (amount)	152,337.769 (424,583.200)	20,910.996 (179,286.300)
At the best ask	61,495.915 (200,446.100)	8893.253 (58,117.880)
Number of buy cancelation (amount)	105,302.057 (300,065.794)	21,881.671 (186,640.627)
At the best bid	28,013.202 (107,619.591)	6411.964 (52,131.004)
Number of sell cancelation (amount)	100,014.113 (289,733.737)	20,635.261 (178,480.570)
At the best ask	28,057.712 (107,257.947)	6273.554 (48,641.546)
Minimum ask price	256.052	256.742
Average ask price	255.154	248.950
Maximum ask price	260.421	261.617
Minimum bid price	255.995	255.334
Average bid price	255.102	248.781
Maximum bid price	260.370	260.921
Minimum spread	0.05	0.05
Average spread	0.0523	0.169
Maximum spread	0.295	3.314
Total number of order submitted	590,363.162	86,210.996

Table 2

The regression results of nearby month contract

	Time	Coeff. (a)	Coeff. (β)	St. error (a)	St. error (β)	t-value (a)	t-value (β)	Prob. (a)	Prob. (β)	$R^{2}$
1 s	9:00–9:30	−1.16E−05	0.000308431	3.44E−05	5.43E−07	−0.3358177	567.9328	0.737009	0	0.4238
	9:30–10:00	−1.29E−05	0.00026682	2.56E−05	4.63E−07	−0.504028	576.8024	0.614242	0	0.437476
	10:00–10:30	1.66E−05	0.000247032	2.47E−05	4.41E−07	0.6702929	560.4511	0.502672	0	0.423021
	10:30–11:00	2.24E−05	0.000251739	2.47E−05	4.78E−07	0.9047585	526.7497	0.365594	0	0.393881
	11:00–11:30	1.55E−05	0.000254518	2.31E−05	4.84E−07	0.6696673	526.4033	0.50307	0	0.397349
	11:30–12:00	−2.56E−05	0.000263739	2.23E−05	4.96E−07	−1.14903	531.6631	0.250544	0	0.408139
	12:00–12:30	−3.94E−05	0.000270222	2.30E−05	5.39E−07	−1.711303	501.3065	0.087026	0	0.384553
	12:30–13:00	−2.33E−05	0.000265028	2.34E−05	5.00E−07	−0.9964812	529.9734	0.319017	0	0.411012
	13:00–13:30	−1.20E−05	0.00026633	2.34E−05	5.03E−07	−0.5127673	529.4779	0.608114	0	0.408458
	13:30–14:00	8.00E−06	0.000251069	2.31E−05	4.60E−07	0.3461488	546.0919	0.729231	0	0.419724
	14:00–14:30	−4.39E−05	0.000252005	2.34E−05	4.44E−07	−1.873841	568.2147	0.060953	0	0.433764
	14:30–15:05	−6.76E−05	0.000241181	2.23E−05	4.14E−07	−3.026797	582.9216	0.002472	0	0.404085
2 s	9:00–9:30	−2.07E−05	0.000309826	6.31E−05	6.30E−07	−0.3282904	491.9402	0.742692	0	0.521726
	9:30–10:00	−1.59E−05	0.000264954	4.46E−05	5.30E−07	−0.356858	499.7088	0.721199	0	0.53006
	10:00–10:30	1.73E−05	0.00024792	4.26E−05	5.02E−07	0.4064994	493.5011	0.684376	0	0.522104
	10:30–11:00	4.51E−05	0.000251959	4.28E−05	5.52E−07	1.05486	456.4552	0.291491	0	0.48326
	11:00–11:30	2.07E−05	0.000256249	3.94E−05	5.55E−07	0.5254908	462.072	0.599243	0	0.49024
	11:30–12:00	−3.48E−05	0.00026478	3.76E−05	5.63E−07	−0.9264851	470.1407	0.354195	0	0.500633
	12:00–12:30	−5.85E−05	0.000273448	3.83E−05	6.12E−07	−1.527524	446.5727	0.126632	0	0.47609
	12:30–13:00	−3.62E−05	0.000264514	3.87E−05	5.64E−07	−0.9359764	469.0799	0.349286	0	0.500701
	13:00–13:30	−1.27E−05	0.000268474	3.96E−05	5.78E−07	−0.3213458	464.4573	0.747949	0	0.494916
	13:30–14:00	2.01E−05	0.000249515	3.89E−05	5.13E−07	0.5169218	486.0022	0.605211	0	0.516577
	14:00–14:30	−8.22E−05	0.000248792	3.98E−05	4.94E−07	−2.064541	503.4815	0.038968	0	0.532851
	14:30–15:05	−0.00011909	0.000239884	3.91E−05	4.74E−07	−3.049558	506.3682	0.002292	0	0.497479
3 s	9:00–9:30	−3.95E−05	0.000307744	9.09E−05	7.03E−07	−0.4347786	437.6944	0.663724	0	0.564276
	9:30–10:00	−1.36E−05	0.000263604	6.33E−05	5.90E−07	−0.2154566	446.659	0.829412	0	0.573994
	10:00–10:30	4.26E−05	0.000247197	6.00E−05	5.60E−07	0.7096022	441.7505	0.477952	0	0.566791
	10:30–11:00	7.70E−05	0.000251644	6.07E−05	6.21E−07	1.268023	405.4673	0.204792	0	0.524296
	11:00–11:30	2.85E−05	0.000255757	5.59E−05	6.23E−07	0.5088014	410.6088	0.610892	0	0.530831
	11:30–12:00	−5.43E−05	0.000262106	5.28E−05	6.29E−07	−1.027004	416.6255	0.30442	0	0.538833
	12:00–12:30	−9.30E−05	0.000274455	5.42E−05	6.90E−07	−1.714201	397.9964	0.086494	0	0.51642
	12:30–13:00	−5.32E−05	0.000262085	5.43E−05	6.28E−07	−0.9794141	417.1203	0.327377	0	0.539798
	13:00–13:30	−1.17E−06	0.00026789	5.59E−05	6.47E−07	−0.020933	414.1903	0.983299	0	0.535985
	13:30–14:00	5.57E−05	0.000246589	5.49E−05	5.69E−07	1.01447	433.0888	0.31036	0	0.557643
	14:00–14:30	−0.000121701	0.000247132	5.62E−05	5.49E−07	−2.165794	450.4235	0.030328	0	0.576452
	14:30–15:05	−0.000170274	0.000239989	5.57E−05	5.31E−07	−3.057349	451.5805	0.002233	0	0.540716
5 s	9:00–9:30	−0.000105347	0.000307116	0.000147075	8.49E−07	−0.7162786	361.5585	0.473821	0	0.595861
	9:30–10:00	−4.99E−06	0.000259108	9.79E−05	6.89E−07	−0.0509414	376.2192	0.959372	0	0.614287
	10:00–10:30	8.66E−05	0.000245165	9.36E−05	6.60E−07	0.9247047	371.3735	0.355122	0	0.606244
	10:30–11:00	0.000119674	0.000249021	9.66E−05	7.43E−07	1.23836	335.2154	0.215586	0	0.556459
	11:00–11:30	3.79E−05	0.000255988	8.87E−05	7.42E−07	0.4271193	345.0843	0.669293	0	0.570854
	11:30–12:00	−6.66E−05	0.000260089	8.23E−05	7.37E−07	−0.8083305	353.0769	0.418903	0	0.582462
	12:00–12:30	−0.000148293	0.00027164	8.59E−05	8.19E−07	−1.726994	331.7998	0.084172	0	0.55212
	12:30–13:00	−5.58E−05	0.000259236	8.54E−05	7.46E−07	−0.6529673	347.364	0.513779	0	0.574695
	13:00–13:30	−2.76E−05	0.000263598	8.87E−05	7.73E−07	−0.3113016	341.2061	0.755572	0	0.565657
	13:30–14:00	0.000103314	0.000242766	8.61E−05	6.67E−07	1.200365	363.7882	0.230001	0	0.596616
	14:00–14:30	−0.000183179	0.000243654	8.83E−05	6.42E−07	−2.074097	379.6701	0.038073	0	0.616771
	14:30–15:05	−0.000259687	0.000237008	8.79E−05	6.24E−07	−2.954382	379.6782	0.003134	0	0.580765
10 s	9:00–9:30	−0.000175555	0.000304679	0.000284316	1.11E−06	−0.6174637	273.6511	0.536932	0	0.628778
	9:30–10:00	2.83E−06	0.000255258	0.000181713	8.79E−07	0.01556993	290.5401	0.987578	0	0.655036
	10:00–10:30	0.000136691	0.000242237	0.000174167	8.42E−07	0.7848272	287.8596	0.432559	0	0.648995
	10:30–11:00	0.000250785	0.000249905	0.00018837	9.98E−07	1.331345	250.3261	0.183082	0	0.583021
	11:00–11:30	6.68E−05	0.000253327	0.000169415	9.66E−07	0.3942955	262.1657	0.693365	0	0.605308
	11:30–12:00	−9.79E−05	0.000256419	0.000155562	9.47E−07	−0.629156	270.9006	0.52925	0	0.620851
	12:00–12:30	−0.000265747	0.000270123	0.000164571	1.08E−06	−1.614791	250.8978	0.106363	0	0.584124
	12:30–13:00	−0.000143173	0.000256065	0.000159395	9.62E−07	−0.8982282	266.2393	0.369069	0	0.612657
	13:00–13:30	−3.62E−05	0.000263357	0.000174011	1.04E−06	−0.2081622	254.2658	0.835103	0	0.590588
	13:30–14:00	0.000167952	0.00023628	0.000162605	8.54E−07	1.032884	276.7982	0.301664	0	0.630931
	14:00–14:30	−0.000346076	0.000239657	0.000166996	8.27E−07	−2.072363	289.8353	0.038237	0	0.652095
	14:30–15:05	−0.000543944	0.000234568	0.000166219	8.01E−07	−3.272445	292.7043	0.001067	0	0.621502
3 min	9:00–9:30	−0.004234629	0.000261608	0.004804091	3.49E−06	−0.8814632	74.93407	0.378163	0	0.716569
	9:30–10:00	−0.000466794	0.000229897	0.002794088	2.57E−06	−0.1670648	89.28983	0.867333	0	0.763617
	10:00–10:30	0.002961479	0.000209084	0.002551122	2.31E−06	1.160853	90.34039	0.245813	0	0.766516
	10:30–11:00	0.004199384	0.00022626	0.002809297	2.91E−06	1.494817	77.71603	0.135089	0	0.708248
	11:00–11:30	0.000665484	0.000227417	0.002725127	2.99E−06	0.244203	76.06784	0.807094	0	0.699311
	11:30–12:00	−0.001033886	0.000222823	0.002391565	2.87E−06	−0.4323051	77.70492	0.665557	0	0.708189
	12:00–12:30	−0.005802797	0.000242884	0.002508107	3.20E−06	−2.313616	75.7921	0.02077	0	0.697781
	12:30–13:00	−0.002130673	0.000240646	0.002593467	3.25E−06	−0.8215539	73.97853	0.41141	0	0.68747
	13:00–13:30	0.00016313	0.000234222	0.002517825	3.11E−06	0.06479001	75.34921	0.948346	0	0.695304
	13:30–14:00	0.00275749	0.00021057	0.002570081	2.64E−06	1.072919	79.75693	0.283411	0	0.718844
	14:00–14:30	−0.005904827	0.000221399	0.002552915	2.56E−06	−2.312974	86.44979	0.020805	0	0.75024
	14:30–15:05	−0.007054675	0.000204142	0.00240204	2.32E−06	−2.936951	87.82734	0.003338	0	0.705819
30 min	9:00–10:00	−0.04419741	0.000218678	0.0435677	8.18E−06	−1.014454	26.73375	0.311371	0	0.745487
	10:00–11:00	0.009067849	0.000185064	0.01691075	3.87E−06	0.5362179	47.83204	0.592051	0	0.823608
	11:00–12:00	0.01431959	0.000195061	0.01782437	5.00E−06	0.8033716	38.99656	0.422148	0	0.755556
	12:00–13:00	−0.02785697	0.000195013	0.01758108	6.16E−06	−1.584486	31.6458	0.113725	0	0.670114
	13:00–14:00	−0.009213474	0.000211047	0.01780186	5.73E−06	−0.5175569	36.84773	0.605001	0	0.734813
	14:00–15:05	−0.0268285	0.000197247	0.01250651	3.66E−06	−2.145162	53.96083	0.032186	0	0.748571
1 h		−0.02506588	0.000185546	0.0132814	2.54E−06	−1.887293	73.01988	0.059289	0	0.75606

Fig. 2.

The $R^{2}$ and the price impact coefficient for the nearby month contract. This shows that the OFI measure explains the price change of the nearby month contracts reasonably well. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/RDA-150113.)

Two different auctions are used in the KOSPI 200 index futures market – a single price call auction and a continuous one. At 9:00 AM, it runs a single price call auction with orders accumulated from 8:00 AM to the auction time. A continuous auction starts right after the first single price call auction and stops at 3:05 PM.6

⁶

The stock market in the Korea Exchange closes the continuous time call auction 15 minutes earlier than the futures market at 2:50 PM.

The second single price call auction clears the market at 3:15 PM with orders accumulated until then. The order execution during the continuous auction is subject to the priority of the price and the time.

During the continuous auction, traders observe cumulated order amounts at the five consecutive price levels of the both sides from the best quote each. A trader can submit 4 different types of orders: a market order, a limit order, a conditional limit order, and a best limit order. A market order has higher priority than other types of orders. A limit order, a conditional limit order, and a best limit order require the same information: the quote price and the amount. A conditional limit order is a limit order, but it will be converted into a market order if it is not executed until the second call auction. A best limit is also a limit order whose price is determined by the best price of the opposite side when the order is submitted. The Korea Exchange (KRX) allows a conditional limit order and a best limit order only for the nearby month contract to prevent price distortion of other contracts. Besides, an order can have either the Fill-Or-Kill (FOK) condition or the Immediate-Or-Cancel (IOC) condition. An order with the FOK condition will be cancelled unless all contracts are executed immediately. For an order with the IOC condition, any portion of the order which cannot be executed is cancelled. If the market does not provide the full amount, the order will be filled only with the available amount, and any portion that is not filled will be cancelled immediately.

Our data set consists of a time-stamped sequence of transactions and quotes for the KOSPI 200 futures, provided by the Korea Research Data Services (KRDS).7

⁷

KOSCOM, a subsidiary of the Korea Exchange, has launched the KRDS since 2012, which provides the transaction and quote data for stocks, derivatives ELW and ETF.

It spans from March 11, 2011 to March 8, 2012. We extract market orders and limit orders within the best five quotes by matching the transaction data and the quote data. We explain the matching algorithm with trades and quotes of KRDS data in detail in the Appendix. We divide the time interval of the continuous auction into sub-intervals as mentioned earlier. The order flow imbalance measure on each sub-interval is calculated based on the transaction and the limit order data. Table 1 gives the summary statistics of the traders and orders in our data set.

Fig. 3.

The $R^{2}$ and the price impact coefficient for the second nearby month contract. The $R^{2}$ of the second month contract is lower than that of the nearby month contract and they are not higher than 15% for any choice of time interval. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/RDA-150113.)

Fig. 4.

The scatter plot for the nearby month contract – 3 minutes scale. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/RDA-150113.)

2.3. Regression analysis

As in Eq. (2), we assume a linear relationship between the OFI measure and the price change. Figure 2 shows that the OFI measure explains the price change of the nearby month contracts reasonably well.8

⁸
Table 2 reports the regression results of the nearby month contract for subinterval.

The

R^{2}

(the left axis) is measured at different sampling time intervals, and it increases as the time interval increases. The predictability increases as the time scale reaches around 3 minutes, and stays near 70% after that. The estimated price impact coefficient (the right axis) is stable for time scales longer than 1 minute, and it shows that the nearby month KOSPI 200 index futures market is highly liquid.

We suspect that a similar result as Fig. 2 occurs in other highly liquid markets. This leads us to test the same relationship with the second month contract and to compare the result to that of the nearby month contract. Figure 3 reports the regression result of the second nearby month contract. Compared to Fig. 2, $R^{2}$ of the second month contract is lower than that of the nearby month contract: the values are not higher than 15% for any choice of time interval. Figure 3 has a hump at the interval of 1 minute, and this phenomenon is similar to Fig. 12 in [7]. The price impact coefficient of Fig. 3 decreases relatively faster as time interval gets longer than 10 seconds.

It is likely that the lower price predictability and the hump shape in Fig. 3 are due to the difference of liquidity characteristics between the nearby month contract and the second nearby month contract. To verify this idea, we plot scatter diagrams in Figs 4 and 5. Figure 4 is for the nearby month contract with the sampling time interval of 3 minutes and Fig. 5 is for the second month contract with the time interval of 3 minutes. Compared to Fig. 4, many points are further deviated in the vertical direction from the regression line in Fig. 5. This implies that the second month contract tends to have large price change without accompanying a limit order flow at the best quotes. This could happen when the limit order book is shallow and has large price gaps between the current best price and the current next best price (see e.g. [10] or [34]).

Fig. 5.

The scatter plot for the second month contract – 3 minutes scale. Compared with Fig. 4, we observe that many points are far deviated in the vertical direction from the regression line. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/RDA-150113.)

If a market is not liquid, the price impact model like CKS does not work well any more as we observe a negative (positive) OFI value and positive (negative) price change in Fig. 5. A shallow limit order book allows a small amount of market order to bite limit orders from the best quote successively. If this event attracts a number of more aggressive limit orders on the opposite side from liquidity traders who are sensitive to the execution probability, the negative (positive) OFI value may be observed even with positive (negative) price change ([11,30] or [31]).9

⁹

An extreme case is so-called ‘fleeting orders’. An interested reader could refer to [20] for this issue.

A shallow limit order market has too many venues and rooms to restrict the response to order book events. So we claim that a price impact model in an illiquid market tends to be more complex to accommodate those possibility. One example is given in [9, Section 7], where the dynamic of price gaps in the limit order book is modeled by a linear regression on the past order flow.

We recall that the linear relation (2) fits worse when the sampling time interval becomes shorter in both Fig. 2 and in Fig. 3. We relate this with another dimension of liquidity: resiliency.10

¹⁰

Kyle [25] describes the liquidity of a market with the bid-ask spread, the depth, and the resiliency.

Even though it is relatively highly liquid, the nearby month KOSPI 200 index futures market may still face a slow resiliency speed or stale quotes in a high-frequency world, where events occur within seconds. Since the next month contract has lower liquidity than the nearby month contract, we focus on the market for the nearby month contract in the next section to highlight the effect of the dynamic behavior of order book events on price changes.

3. Discussion of the CKS model

3.1. VAR analysis

As we see in Figs 2, 4 and 7, the observed pair of the OFI value and the price change in the market for the nearby month contract tends to get closer to the regressions line in Eq. (2). This leads us to suspect that there is a lagged price change induced by the order flow imbalance or the causality to the other direction.

We can verify this idea by performing the causality test by Granger [17]. We first introduce a vector autoregressive model (VAR model) as follows: $\begin{matrix} (3) & x_{t} = A_{0} + \sum_{i = 1} A_{i} x_{t - i}, x_{t} = [\begin{matrix} Δ P_{t} \\ {OFI}_{t} \end{matrix}], \end{matrix}$ where $A_{i}$ ’s are coefficient matrices ( $i = 0, 1, \dots$ ). We estimate the VAR model (3) and investigate whether the coefficients are different from zero or not. The null hypothesis is that there is no causality from one variable to the other.

Before performing the causality test, we use the augmented Dickey–Fuller test to check whether the time series admits a unit root. We do not report the result, but both the series of the OFI value and the series of mid-price change do not have a unit root each day and each subinterval at the significance level of 1%. Then, we use the Schwarz information criterion (SIC) to choose the maximum time lag. This test leads us to set 3 for a short timescale and 1 for a longer timescale.

Fig. 6.

The ratio of the days on which the hypothesis of no causality is rejected. The dashed line is the case in which the price change causes the order flow imbalance, the dotted line is for the other direction and the solid line is for bilateral causality. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/RDA-150113.)

Finally, we count the number of days on which we can reject the null hypothesis of no causality from one variable to the other, or in total. Figure 6 shows the ratio of the number of days on which we can reject the null hypothesis at the significance level of 10%. The dashed line is the case in which the price change causes the order flow imbalance, and the dotted line is for the other direction. We see that the OFI causes the price change for time intervals less than 20 seconds. This explains the observations for which the OFI measure is too large relative to a small price return in absolute values. Similarly, the price change causes the change of the OFI for time intervals less than 10 seconds. The figure also shows that the causality from the OFI to the price change tends to be stronger (weaker) than that from the price change to the change of OFI for time intervals less (more) than 1 minute.

Table 3

The multiple linear regression results of nearby month contract

	Time	Coeff. ( $β_{0}$ )	Coeff. ( $β_{1}$ )	Coeff. ( $β_{2}$ )	Coeff. ( $β_{3}$ )	Prob. ( $β_{0}$ )	Prob. ( $β_{1}$ )	Prob. ( $β_{2}$ )	Prob. ( $β_{3}$ )	$R^{2}$
1 s	9:00–9:30	0.000313479	−1.67E−05	−8.98E−06	−4.96E−06	0	3.48E−180	8.06E−54	1.16E−18	0.4258939
	9:30–10:00	0.000270861	−1.85E−05	−9.14E−06	−6.07E−06	0	0	5.01E−81	4.50E−38	0.4408138
	10:00–10:30	0.000249998	−1.45E−05	−7.59E−06	−5.65E−06	0	1.80E−223	1.66E−62	1.69E−36	0.4254801
	10:30–11:00	0.000254539	−1.53E−05	−5.69E−06	−5.15E−06	0	3.58E−213	4.68E−31	2.11E−26	0.3959165
	11:00–11:30	0.00025724	−1.44E−05	−6.29E−06	−4.34E−06	0	3.40E−185	7.76E−37	7.76E−19	0.3992037
	11:30–12:00	0.000267145	−1.70E−05	−6.41E−06	−3.99E−06	0	4.77E−242	6.07E−36	2.30E−15	0.4104287
	12:00–12:30	0.000272844	−1.40E−05	−4.93E−06	−4.56E−06	0	9.13E−141	5.70E−19	7.67E−17	0.3859592
	12:30–13:00	0.000268259	−1.68E−05	−8.36E−06	−5.71E−06	0	6.25E−233	1.52E−59	1.80E−29	0.4135815
	13:00–13:30	0.000269182	−1.42E−05	−7.95E−06	−3.80E−06	0	3.21E−165	3.08E−53	9.24E−14	0.4103267
	13:30–14:00	0.00025537	−1.75E−05	−8.10E−06	−3.72E−06	0	2.98E−292	6.92E−64	2.41E−15	0.4226969
	14:00–14:30	0.000256741	−1.95E−05	−6.61E−06	−5.70E−06	0	0	4.91E−46	2.84E−36	0.4372973
	14:30–15:05	0.000245009	−1.74E−05	−4.13E−06	−4.33E−06	0	0	7.98E−22	9.29E−25	0.4066452
2 s	9:00–9:30	0.000313459	−2.10E−05	−5.50E−06	−5.52E−06	0	7.57E−233	1.42E−17	4.47E−18	0.524665
	9:30–10:00	0.000267741	−2.21E−05	−6.17E−06	−4.01E−06	0	0	9.43E−31	4.69E−14	0.5344089
	10:00–10:30	0.000250077	−1.94E−05	−5.06E−06	−3.66E−06	0	0	1.45E−23	3.53E−13	0.5258147
	10:30–11:00	0.000253773	−1.66E−05	−5.01E−06	−2.80E−06	0	5.69E−196	2.29E−19	4.17E−07	0.4857409
	11:00–11:30	0.000258159	−1.60E−05	−5.68E−06	−1.63E−06	0	6.66E−180	3.17E−24	0.00344015	0.4925563
	11:30–12:00	0.000266999	−1.82E−05	−6.51E−06	−2.50E−06	0	7.33E−224	2.64E−30	9.39E−06	0.5035348
	12:00–12:30	0.000275257	−1.53E−05	−5.38E−06	−2.13E−06	0	4.43E−134	3.36E−18	0.00054567	0.4778895
	12:30–13:00	0.000266814	−2.14E−05	−5.21E−06	−3.63E−06	0	0.00E+00	4.46E−20	1.29E−10	0.5043805
	13:00–13:30	0.000270706	−1.79E−05	−5.92E−06	−2.87E−06	0	6.58E−206	3.76E−24	7.71E−07	0.497589
	13:30–14:00	0.000252622	−2.01E−05	−5.09E−06	−3.69E−06	0	0	1.63E−22	8.85E−13	0.5204719
	14:00–14:30	0.000251847	−2.03E−05	−6.54E−06	−3.13E−06	0	0	8.58E−39	2.92E−10	0.5371436
	14:30–15:05	0.000242185	−1.61E−05	−4.55E−06	−3.39E−06	0	2.86E−245	2.66E−21	1.08E−12	0.5001737
3 s	9:00–9:30	0.000310147	−1.87E−05	−6.36E−06	−6.62E−06	0	3.05E−153	2.75E−19	6.55E−21	0.5671196
	9:30–10:00	0.000265534	−2.19E−05	−5.45E−06	−4.43E−06	0	1.63E−299	2.80E−20	5.18E−14	0.578537
	10:00–10:30	0.000248809	−1.82E−05	−4.70E−06	−4.88E−06	0	5.57E−230	5.36E−17	2.46E−18	0.5704399
	10:30–11:00	0.000253062	−1.68E−05	−4.34E−06	−2.96E−06	0	3.88E−160	2.99E−12	1.93E−06	0.5269587
	11:00–11:30	0.000257462	−1.60E−05	−3.70E−06	−5.10E−06	0	9.75E−144	3.41E−09	2.97E−16	0.5333667
	11:30–12:00	0.000263913	−1.73E−05	−4.50E−06	−4.59E−06	0	4.14E−164	1.03E−12	3.14E−13	0.5416465
	12:00–12:30	0.000276047	−1.59E−05	−2.96E−06	−4.44E−06	0	5.77E−116	2.03E−05	1.34E−10	0.5184031
	12:30–13:00	0.000263481	−1.89E−05	−4.63E−06	−3.71E−06	0	8.15E−197	1.74E−13	3.33E−09	0.5429206
	13:00–13:30	0.000269643	−1.75E−05	−4.86E−06	−4.45E−06	0	7.75E−159	7.87E−14	6.08E−12	0.5387348
	13:30–14:00	0.000248828	−1.84E−05	−4.56E−06	−3.65E−06	0	4.92E−224	1.87E−15	1.63E−10	0.5611926
	14:00–14:30	0.000249564	−2.04E−05	−4.00E−06	−3.89E−06	0	6.42E−297	4.54E−13	1.42E−12	0.5808449
	14:30–15:05	0.000241795	−1.54E−05	−4.46E−06	−2.84E−06	0	4.52E−181	7.91E−17	9.50E−08	0.5433525
5 s	9:00–9:30	0.000309565	−1.79E−05	−9.63E−06	−9.50E−06	0	3.82E−97	1.59E−29	5.87E−29	0.5994455
	9:30–10:00	0.000260897	−1.82E−05	−6.83E−06	−5.33E−06	0	5.36E−154	3.89E−23	9.22E−15	0.6183088
	10:00–10:30	0.000246843	−1.75E−05	−5.97E−06	−5.67E−06	0	1.00E−154	1.57E−19	8.37E−18	0.6102868
	10:30–11:00	0.000250161	−1.40E−05	−4.78E−06	−4.58E−06	0	2.51E−78	1.31E−10	6.86E−10	0.5586971
	11:00–11:30	0.000257517	−1.46E−05	−5.56E−06	−4.61E−06	0	2.14E−85	8.50E−14	5.42E−10	0.5733581
	11:30–12:00	0.000261767	−1.59E−05	−5.75E−06	−5.37E−06	0	4.76E−102	7.36E−15	3.26E−13	0.5853637
	12:00–12:30	0.00027301	−1.40E−05	−4.68E−06	−4.41E−06	0	2.46E−65	1.22E−08	7.41E−08	0.5540114
	12:30–13:00	0.000260316	−1.66E−05	−6.23E−06	−2.04E−06	0	1.99E−109	6.89E−17	0.006208619	0.5774581
	13:00–13:30	0.000264947	−1.48E−05	−5.08E−06	−2.59E−06	0	4.43E−81	5.88E−11	0.000809852	0.5678185
	13:30–14:00	0.000244788	−1.69E−05	−3.83E−06	−5.35E−06	0	2.09E−139	1.13E−08	1.16E−15	0.6001046
	14:00–14:30	0.000245558	−1.69E−05	−5.78E−06	−4.75E−06	0	9.80E−151	2.56E−19	1.37E−13	0.6205831
	14:30–15:05	0.000238612	−1.43E−05	−3.79E−06	−5.42E−06	0	2.80E−115	1.47E−09	4.35E−18	0.5835132
10 s	9:00–9:30	0.000308351	−2.38E−05	−1.24E−05	−1.09E−05	0	2.21E−100	1.83E−28	1.11E−22	0.6352214
	9:30–10:00	0.000257702	−1.89E−05	−7.51E−06	−4.66E−06	0	6.58E−101	1.82E−17	1.13E−07	0.6598049
	10:00–10:30	0.000244389	−1.74E−05	−9.22E−06	−4.18E−06	0	1.21E−94	8.78E−28	6.57E−07	0.653921
	10:30–11:00	0.000251457	−1.53E−05	−5.30E−06	−5.95E−06	0	1.84E−52	1.24E−07	2.52E−09	0.5859861
	11:00–11:30	0.00025489	−1.44E−05	−7.10E−06	−4.22E−06	0	2.13E−49	2.57E−13	1.29E−05	0.6080745
	11:30–12:00	0.000258337	−1.71E−05	−7.33E−06	−5.93E−06	0	5.95E−72	1.19E−14	3.62E−10	0.6247372
	12:00–12:30	0.000271824	−1.38E−05	−6.43E−06	−5.29E−06	0	3.76E−37	2.92E−09	9.24E−07	0.5863625
	12:30–13:00	0.00025729	−1.50E−05	−6.51E−06	−4.37E−06	0	1.58E−54	1.42E−11	5.52E−06	0.6154022
	13:00–13:30	0.000264876	−1.47E−05	−6.05E−06	−6.38E−06	0	2.84E−45	5.72E−09	7.67E−10	0.593287
	13:30–14:00	0.000238244	−1.43E−05	−6.86E−06	−3.47E−06	0	1.72E−61	1.59E−15	5.07E−05	0.6341163
	14:00–14:30	0.000241937	−1.78E−05	−6.35E−06	−4.23E−06	0	7.63E−101	2.42E−14	3.09E−07	0.6567113
	14:30–15:05	0.000236243	−1.39E−05	−7.14E−06	−5.90E−06	0	2.04E−66	7.70E−19	1.88E−13	0.6249745
20 s	9:00–9:30	0.00030086	−2.92E−05	−1.22E−05	−7.09E−06	0	1.35E−89	4.47E−17	8.60E−07	0.6651872
	9:30–10:00	0.000251734	−1.87E−05	−8.69E−06	−5.63E−06	0	6.61E−61	1.55E−14	5.55E−07	0.6928022
	10:00–10:30	0.000240829	−2.08E−05	−7.92E−06	−4.05E−06	0	6.49E−82	2.10E−13	0.000164709	0.6918251
	10:30–11:00	0.000248145	−1.75E−05	−4.94E−06	−4.98E−06	0	8.32E−41	0.000159116	0.000135917	0.6178005
	11:00–11:30	0.000253747	−1.72E−05	−8.29E−06	−5.26E−06	0	8.93E−41	1.07E−10	4.06E−05	0.6368433
	11:30–12:00	0.000254234	−2.01E−05	−6.27E−06	−1.06E−05	0	3.28E−60	3.00E−07	4.55E−18	0.6591611
	12:00–12:30	0.000266925	−1.42E−05	−7.41E−06	−5.31E−06	0	2.12E−24	9.43E−08	0.000123397	0.624043
	12:30–13:00	0.000255507	−1.73E−05	−8.63E−06	−1.45E−06	0	2.95E−42	9.60E−12	0.250691318	0.6458145
	13:00–13:30	0.000263596	−1.87E−05	−6.03E−06	−8.15E−06	0	3.57E−39	2.42E−05	1.07E−08	0.6043647
	13:30–14:00	0.00023546	−1.60E−05	−7.31E−06	−5.41E−06	0	6.50E−44	1.92E−10	2.10E−06	0.6555863
	14:00–14:30	0.000234309	−1.63E−05	−6.82E−06	−5.95E−06	0	1.79E−53	1.19E−10	1.80E−08	0.6874468
	14:30–15:05	0.000231466	−1.71E−05	−5.78E−06	−5.66E−06	0	3.70E−60	2.81E−08	4.90E−08	0.6550789
30 s	9:00–9:30	0.000295839	−3.28E−05	−8.96E−06	−4.87E−06	0	1.56E−80	1.72E−07	0.004160022	0.675598
	9:30–10:00	0.000249567	−2.02E−05	−9.02E−06	−6.01E−06	0	7.19E−54	3.91E−12	3.37E−06	0.7159464
	10:00–10:30	0.000233214	−1.93E−05	−6.28E−06	−4.53E−06	0	2.70E−53	5.48E−07	0.000277711	0.7019701
	10:30–11:00	0.000247084	−1.56E−05	−9.06E−06	−5.73E−06	0	6.11E−22	2.10E−08	0.000376419	0.6117475
	11:00–11:30	0.000253103	−1.87E−05	−7.50E−06	−5.45E−06	0	4.90E−34	1.04E−06	0.000372382	0.6471569
	11:30–12:00	0.000248816	−1.79E−05	−1.06E−05	−6.59E−06	0	1.20E−35	1.33E−13	3.87E−06	0.6709051
	12:00–12:30	0.000268049	−1.64E−05	−9.82E−06	−3.16E−06	0	2.55E−21	1.26E−08	0.065936885	0.6199606
	12:30–13:00	0.000251584	−1.70E−05	−6.35E−06	−3.17E−06	0	9.30E−31	1.67E−05	0.031381512	0.6624046
	13:00–13:30	0.000262	−1.60E−05	−1.25E−05	−3.05E−06	0	1.41E−20	2.69E−13	0.074231664	0.6111736
	13:30–14:00	0.000232661	−1.53E−05	−7.46E−06	−4.37E−06	0	9.76E−29	5.13E−08	0.001322646	0.6622377
	14:00–14:30	0.000230923	−1.63E−05	−8.16E−06	−5.62E−06	0	4.20E−40	3.14E−11	4.43E−06	0.7045421
	14:30–15:05	0.000226485	−1.70E−05	−7.64E−06	−1.70E−06	0	1.77E−44	2.68E−10	0.157827781	0.6678064

Based on the existence of lagged effects for short time intervals, we consider the multiple linear regression model: $\begin{array}{rcl} Δ P_{t} & = & α + β_{0} {OFI}_{t} + β_{1} {OFI}_{t - 1} + β_{2} {OFI}_{t - 2} \\ (4) & + β_{3} {OFI}_{t - 3} + ϵ_{t}, \end{array}$ where the lag length is set to be 3 as in the result of SIC test. Table 3 shows that the change of mid-prices of the nearby contract is significantly related to lagged OFI measures for each time interval and the $R^{2}$ on average increases by 0.65%. It implies that the high frequency trader has to keep in mind the lagged effect of the OFI measures to price changes.

Fig. 7.

The scatter plot – 10 seconds scale. Comparing this with Fig. 4, we have relatively many points far from the regression line. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/RDA-150113.)

3.2. Limit order activity

Figure 7 shows the scatter plot of the nearby month contract for the sampling interval of 10 seconds. Comparing this to Fig. 4 which is the scatter plot for the time interval of 3 minutes and shows that the model fits data well, we have relatively many points far from the regression line in Fig. 7. One possible reason is the discrepancy of response time between the mid-price change and the order flow imbalance. According to [21, Fig. 13], the impulse response of mid-price to trade is far faster than that to an equal-size limit order shock at the best quotes, that is consistent with the prediction by Roşu [32]. If the length of sampling interval is too short, the mid-price could not fully reflect the effect of limit order events.

We claim that limit order activities become more frequent than trading activities in a high frequency domain, so the discrepancy of the response time gets more exacerbated. We introduce the limit order activity ratio (LOAR) for comparing with the trading activity in a market as follows: $\begin{matrix} (5) & {LOAR}_{t} ≜ \{\begin{matrix} 0 if L_{t}^{b} - C_{t}^{b} - L_{t}^{s} + C_{t}^{s} = 0, \\ \frac{| L_{t}^{b} - C_{t}^{b} - L_{t}^{s} + C_{t}^{s} |}{| M_{t}^{b} - M_{t}^{s} | + | L_{t}^{b} - C_{t}^{b} - L_{t}^{s} + C_{t}^{s} |} \\ otherwise . \end{matrix} \end{matrix}$ The denominator of the limit order activity ratio corresponds to the subtraction of the trade imbalance from OFI measure in [7]. So high (low) limit order activity ratio means relatively large (small) contribution of limit orders in the observed order flow imbalance.

The solid (dotted) line in Fig. 8 shows the probability distribution function of the limit order activity ratio of the nearby month contract for the time interval of 3 minutes (10 seconds). The distribution of the time interval of 10 seconds is shifted to the right from that of the 3 minute interval. This implies the following. For a shorter time interval, we have higher probability to get the shock generated by limit orders than by market orders given the same OFI measure, those two shocks are about even while for a longer time interval. Since the response time of a price change to limit orders is relatively slow as Hautsch, Huang and Roşu show, a mid-price change due to order submission may not occur during that short time interval.

Fig. 8.

Limit order activity ratio. The solid (dotted) line shows the probability distribution function of the limit order activity ratio of the nearby month contract for the time interval of 3 minutes (10 seconds). (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/RDA-150113.)

4. Conclusion

We tested the effect of order book events at best quotes on the price change with the model proposed by Cont et al. [7]. The OFI measure reasonably explains well the price change of the nearby month KOSPI 200 futures contract for the longer sampling time. On the other hand, the CKS model does not fit well with the second nearby month KOSPI 200 futures. We suspect that it is because the one is highly liquid while the other is not. The scatter diagrams shows that a shallow limit order market has too many venues and rooms to restrict the response to order book events.

Even when a market admits narrow bid-ask spreads and high depths, a price impact model like the CKS model may fail to explain the high-frequency behavior of price change. As sampling time interval gets shorter, the delay of information due to the limit of response time may hinder the accuracy of the CKS model. In a high-frequency region, the activity of limit orders given an order flow imbalance tends to get stronger than that of transactions. This is a reason why we observe the delayed response between the price change and the order flow imbalance verified by the Granger-causality test with a VAR model.

We conclude that the lack of liquidity in a market of the information of the dynamic in a high-frequency region of a market could erode the validity of the CKS model. A price impact model of order book events needs to be sophisticated to accommodate an illiquid market or high-frequency price behavior of a market. In this sense, the validity of the CKS model should be restricted only to a liquid market for a med-frequency or a low-frequency region as opposed to [7, p. 3] intend to model the instantaneous impact of order book events. It is also not surprising that Hautsch and Huang [21] report the difference between the short-run and long-run impact of incoming limit orders, and that Eisler et al. [9] try to model the dynamic of price gaps in the limit order book using a linear regression on the past order flow.

Table 4

Sample transaction data and quote data

Date	Time	SN	Name	TSA	BAP	OA	SBAP	OA	$\dots$
Panel A: Sample order data
20110311	10:17:43:125	189051	KR4101F60005	8313	258.35	23	258.3	50	$\dots$
20110311	10:17:43:135	189052	KR4101F60005	8316	258.35	26	258.3	50	$\dots$
20110311	10:17:43:136	189053	KR4101F60005	8314	258.35	24	258.3	50	$\dots$
20110311	10:17:43:137	189054	KR4101F60005	8309	258.35	19	258.3	50	$\dots$
20110311	10:17:43:139	189055	KR4101F60005	8305	258.35	15	258.3	50	$\dots$
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮

Date	Name	TP	TA	Time	CTA	BS	SN
Panel B: Sample transaction data
20110311	KR4101F60005	258.35	2	10:17:43:086	125,072	1	189053
20110311	KR4101F60005	258.35	5	10:17:43:095	125,077	1	189054
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮

Notes: SN – serial number; TSA – total sell amounts; BAP – best ask price; OA – outstanding amount; SBAP – the second best ask price; TP – transaction price; TA – transaction amount; CTA – cumulative transaction amount; BS – buy or sell.

Footnotes

Acknowledgements

This research was supported by WCU (World Class University) program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (R31-20007).

KRDS data processing

States of the limit order book in KRDS are recorded whenever a trade occurs or a submission, cancelation or reorder of limit order within five best quotes occurs. In particular, if the trader submits a market order and it is executed, it is recorded to transaction data with the transaction price and the transaction amount. Quote data consists of date, time, futures code (name), prices and the amount of 5 consecutive outstanding orders from best prices, and the number of contracts. The transaction data includes information like date, time, futures code, transaction price, transaction amount, and the cumulative transaction amounts and trading volume (see Table 4).

Since we observes the state of the limit order book from quote data, we do not directly know whether a decrease of the total amount is due to a cancelation order or a market order with the same function. But by matching the message serial numbers11

¹¹

This is the number increasing by 1 when each order is submitted and is useful to distinguish a cancelation order and a market order. If a market order with larger amount than outstanding amounts at the best price is submitted, then the message serial number is the biggest tick which is touched to execute the market order.

from the transaction data and the quote data, we can distinguish those two. Table 4 explains this. The upper one of Table 4 is the part of quote data reflecting the state of the limit order book changed by an order submitted at 10:17:43 on March 11 in 2011. The lower one of Table 4 shows information of a transaction by a market order submitted at that time. Because a market order is submitted and executed at 10:17:43:136,12

¹²

We think that the reason the time in transaction data is different to that in quote data for a market order is due to the data transmission time.

the transaction price, transaction amount, and the direction of trade (buy or sell) are recorded to transaction data simultaneously. But the decrease in the amount at 10:17:43:139 is due to a cancelation order, not to a market order. This is why there is no serial number 189055 in transaction data.

The row with time 10:17:43:125 tells us that a sell limit order with 3 contracts at the best ask price is submitted since the outstanding amount in the ask side and the best ask price increase by 3. In this way, we can obtain information about limit orders at the specific price level and tell a cancelation order from a market order. In the case of price revision we can consider this as the simultaneous occurrence of a limit order and a cancelation. This event is recorded to the quote data without change of the total amount, but with a decrease in the amounts at the specific price level and an increase at another specific price level.

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The effect of limit order flows at the best quotes on price changes

Abstract

Keywords

1. Introduction

1 We cite Parlour and Seppi [29]: “Now in 2007 most equity and derivative exchanges around the world are either pure electronic limit order markets or at least allow for customer limit orders in addition to an on-exchange market making”. See also [23] and [33].

2.1. The CKS model

Table 1 Summary of the trades and orders, the daily average

8 Table 2 reports the regression results of the nearby month contract for subinterval.

3.1. VAR analysis

Footnotes

Acknowledgements

KRDS data processing

References

¹
We cite Parlour and Seppi [29]: “Now in 2007 most equity and derivative exchanges around the world are either pure electronic limit order markets or at least allow for customer limit orders in addition to an on-exchange market making”. See also [23] and [33].

Table 1
Summary of the trades and orders, the daily average

⁸
Table 2 reports the regression results of the nearby month contract for subinterval.