High‐Frequency Price Discovery and Price Efficiency on Interest Rate Futures

• Author: Jing Nie
• DOI: http://doi.org/10.1002/fut.22016
• Published date: 01 November 2019
• Date: 01 November 2019

Received: 1 April 2019

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Revised: 8 April 2019

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Accepted: 9 April 2019

DOI: 10.1002/fut.22016

RESEARCH ARTICLE

High‐Frequency Price Discovery and Price Efficiency on

Interest Rate Futures

Jing Nie

School of Banking and Finance,

University of International Business and

Economics, Beijing, China

Correspondence

Jing Nie, School of Banking and Finance,

University of International Business and

Economics, No. 10, Huixin Dongjie,

Chaoyang District, Beijing 100029, China.

Email: jing.nie@uibe.edu.cn

Abstract

This paper estimates a collection of high‐frequency informational efficiency

metrics by constructing a unique Eurodollar futures data set with the complete

messaging history. To capture price efficiency, this paper calculates the mid‐

quote return autocorrelations following a full range of time intervals. The

findings suggest the mid‐quote return autocorrelations are positive and

gradually increase from the tick‐level to 30‐min. Then, I utilize a vector

autoregression to estimate the pricing error, which shows the adjustment time

of trade returns is completed in 1 s. Furthermore, trade prices are less sensitive

about incorporating any available new information as the Eurodollar futures

approaches its maturity.

KEYWORDS

impulse response analysis, limit orders, price efficiency, trade classification, vector autoregression

JEL CLASSIFICATIONS

G12, G14

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INTRODUCTION

The speed of access to financial markets through electronic communication networks and the frequency of updating

from automated algorithms is increasing dramatically. For instance, in the Eurodollar futures market, the average

updating speed has dropped from about 20 min to 600 ms from 1996 to 2014. Futures contracts have always been active

and liquid markets; however, their microstructure and the subsequent understanding of how prices are formed

have only recently been brought into focus. This paper provides a comprehensive empirical microstructure analysis on

the price efficiency to answer how fast participants need to be in the Eurodollar (ED) futures market. My approach is to

apply a set of empirical measurements to evaluate both quotes and trades efficient reaction time. This study

demonstrates that the trading reaction time is below 1 s. For contracts close to maturity, the trading reaction time even

within 100 ms. Furthermore, quoting reaction time is faster than trade. For instance, the mid‐quote can incorporate

new information and adjust itself to a relatively efficient price within 15 ms.

One of the motivation is to figure out the high‐frequency price discovery in the ED futures market. With the progress

of technology in the financial markets, the microstructure plays a starring role as its faster trading speed. High‐

frequency trading (HFT) causes some fundamental changes in asset pricing, especially in liquidity and the price

discovery process (Brownlees & Gallo, 2006; O’Hara, 2003; Riordan & Storkenmaier, 2012). For instance, informed

traders no longer only indicate those with access to private inside information and those who take the arbitrage

opportunity; in a high‐frequency world, if some HFTs receive, react, and process information faster than others, they

are also treated as informed traders. Besides the informed trading, HFTs tend to submit large amounts of orders and

then cancel them instead of executing them, which creates a phantom liquidity and gives other traders a false

J Futures Markets. 2019;39:1394–1434.wileyonlinelibrary.com/journal/fut1394

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© 2019 Wiley Periodicals, Inc.

impression about the market liquidity. In this way, some HFTs can result in asymmetric information, decrease the

capacity of the price to incorporate the available information, and eventually harm the market efficiency and increase

trading costs. However, some HFTs also act as liquidity providers, rather than relying on informed trading to gain

profits, so they do have benefits for the market liquidity and decrease the trading costs.

Furthermore, another motivation for this paper studying the microstructure of this particular market is the

significance of the Eurodollar futures market. As one of the most liquid and actively traded contracts in global financial

markets, the 3‐month ED futures contract on the Chicago Mercantile Exchange (CME) does not get enough academic

attention. Besides, the increasing marginal costs and strict regulations on interest rate swaps (IRS) cause the significant

transfer of trading activities from the opaque over‐the‐counter‐IRS to ED strips to construct synthetic swaps.

The large proportion of HFTs among the total traders is another motivation this study focuses on the high‐frequency

price discovery process in the Eurodollar futures market. In my Eurodollar futures data set, 65% of total activity is from

traders at high‐frequency when measured by fraction of messages on the order book at 25 ms or faster, a fraction that is

consistent with the evidence from Group (2010), where 64.46% message updates are from accounts registered as being

automated trading accounts in the 2010 Eurodollar futures market.

The empirical contribution of this paper is fourfold. First, this paper presents one of the first studies utilizing

information from the complete limit order book to assess the impact of high‐frequency transactions on the

instantaneous level of liquidity for the ED futures market. Comprehensive analytical work on data sets of over a billion

observations is still rare in financial economics and econometrics. I construct a unique limit order book data set of

Eurodollar futures from 2008 to 2014, involving $7.66 quintillion ask total volumes, $7.56 quintillion bid total volumes,

and $2 quadrillion trade volumes. When working in the very high‐frequency domain, even computing auto‐correlations

requires careful implementation, and the major innovation of this study is in carefully documenting the appropriate

strategies for this type of analysis.

Secondly, this paper documents the high‐frequency price formation mechanism for the ED futures market, and

discoveries the effectiveness of various trade direction indicators (including a new version designed specifically for this

market) in determining the price direction. To capture the level of price efficiency, this study calculates the absolute

degree of autocorrelation in the mid‐price returns with 26 time‐intervals. Higher absolute magnitudes in returns

indicate persistent fluctuations away from the mid‐price. The findings indicate that the mid‐quoted return

autocorrelations are positive and gradually increase from the shortest time interval to the longest time interval,

except for the negative return autocorrelation at the tick level. Compared with other studies in the same field

(Anderson, Eom, Hahn, & Park, 2013; Chakrabarty, Jain, Shkilko, & Sokolov, 2014; Hendershott & Jones, 2005), most of

them only measure quoted return autocorrelations in seconds or minutes, even at a daily level, because of the challenge

to process massive quantities of microstructure data and the lack of clean processed data from the equity market

according to Brownlees and Gallo (2006).

Pricing models in this study decompose the observed price into the efficient price and the pricing error. To measure

the deviation of the trade prices from the actual efficient prices, this paper implements the vector autoregression (VAR)

to estimate the pricing error and examine the impulse responses of trade return to trade directions, trade volume, the

square root of trade volume, and ask and bid market concentrations

1

. The responses imply that all factors have an

influence on trade returns and the speed of the trade return adjustment is very fast, occurring within 1 s. This also

indicates that the price discovery studies need to be conducted within very short time intervals due to the current high‐

speed trading.

Thirdly, this paper introduces a new trade direction indicator for use in adverse selection and intraday price impact

models, which is specially designed for the Eurodollar futures market and is fundamental to determine buy and sell

trades with very high frequency data. The standard trade direction algorithms implementations, such as the Lee‐Ready

trade direction indicator, appear to give erroneous results. This paper develops a Volume Weighted Average Price

(VWAP) trade classification algorithm from the entire limit order book (buy and sell side) and then identify each trade

as a buy or sell side based on its volume‐weighted position in the order book. The algorithm eliminates the iceberg

trades and utilizes the VWAP over five levels of Eurodollar limit order book to classify trades directions. The efficiency

rate of this algorithm, 95.88%, is three times efficient as the traditional Lee–Ready algorithm using the Eurodollar

futures (see Table 1).

1

As the number of buyers and sellers is significant for shifting trade prices, this paper considers the signed bid‐side and ask‐side market concentrations as dependents on price discovery mechanisms

via the VAR model and impulse response functions

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Finally, this paper documents the degree of predictability inherent in the order‐book as shocks to order‐flow

permeate across the term structure and through time. As one of the major differences between equity and futures is that

the futures has its own time to mature, therefore, this study verifies the maturity effects on the price discovery and

market liquidity for the Eurodollar futures.

The remainder of this paper is structured as follows: Section 2 reviews the relevant high‐speed market

microstructure literature, especially regarding the high‐frequency price discovery. Section 3 presents varying

methodologies and the construction of variables to examine the price discovery in the ED futures market. Section 4

describes the data with descriptive statistics, as well as focuses on the results interpretation with the price discovery and

market liquidity of the ED futures markets. Section 5 summarizes the empirical findings implications in general and

provides some comments.

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THE DYNAMICS OF PRICE DISCOVERY

Market efficiency and market informativeness are the fundamental attributes of financial markets. The purpose of

buying and selling in a continuous limit order book, such as the Globex platform, is to provide a mechanism for

processing information and subsequently to efficiently value the assets in question. As one of the desirable features of

futures markets, the price discovery function is the ability to determine a price that balances the supply and demand for

futures contracts. Prior research utilizes the term ‘price discovery’to describe a variety of empirical characteristics. For

instance, price discovery can be considered as a process of finding an equilibrium price (Schreiber & Schwartz, 1986).

Hasbrouck (1995) defines price discovery as the ability of financial markets to impound new information. Similarly,

Baillie, Booth, Tse, and Zabotina (2002) mention that price discovery reveals the relation between prices and

information from one or multiple markets. Lehmann (2002) describes price discovery as the ability to efficiently

incorporating information (learning from investors trading behavior) into the market prices. These explanations suggest

that price discovery is a dynamic process to reach a state of equilibrium with the rapidly adjusting market prices to

replace the old equilibrium with the new one through new information.

Prior studies mainly utilize four types of measurements to interpret the efficiency of price discovery: The return

autocorrelations (Anderson et al., 2013; Foley and Putniņš, 2016; Hendershott & Jones, 2005), the variance ratio (Castura,

Litzenberger, Gorelick, & Dwivedi, 2010; Lo & MacKinlay, 1988), the price delay (Hou & Moskowitz, 2005), and pricing

error (Hasbrouck, 1993). This study employs both the autocorrelation and the price error methods to assess the efficiency of

price discovery in the Eurodollar futures market and takes the lead in doing so on ultrahigh frequency data.

The first approach, the autocorrelation of mid‐price returns, can reflect the degree of quotes prices deviating from

the random walk, and imply the predictability of short‐term returns (Anderson et al., 2013; Foley & Putniņš, 2016;

TABLE 1 Comparison of trade classification algorithms

GEH0 (June 05, 2009) Lee–Ready algorithm Volume weighted average algorithm

Total asks 7,082,965

Total bids 7,082,965

Total trades 29,793

Buy‐side trades (+1) 4,949 12,741

Sell‐side trades (

−

1) 4,805 15,824

Excluded ask side 98

Excluded bid side 205

Trades direction indicator (

q

)9,754 28,565

Algorithm efficiency ratio 32.74%95.88%

Note: This table compares the trade classification by the Lee–Ready algorithm and the volume weighted average algorithm. This paper examines the full order

flow and executed prices of GEH0 on June 05, 2009 as a toy example to examine the reliability of both trade classification algorithms. Because of 8 months

before GEH0 maturity, this contract is relative active on this day with 29,793 trades observations. Total asks, total bids, and total trades are the total number

observation of asks, bids, and transactions within 1 day. Buy‐side and sell‐side trades report how many trades are classified as buyer‐side (+1) initiated trades or

seller‐side (−1) initiated trades. The volume weighted average trade classification method eliminates the iceberg trades as the outside the spread; therefore the

number of iceberg trade is reported as the excluded ask side and excluded bid side. Trade direction indicators refer to the sum of buy‐side and sell‐side trades,

and algorithm efficiency ratio is the number of trade direction indicator to the total trades.

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