The Fatal Flaw in High-Frequency Trading No One’s Talking About

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Abstract

1. Introduction

   1.1 Periodic auction and continuous limit order book

   1.2 Comparison and main flaws of limit order book

   1.3 Optimal policies to cure auction’s inefficiencies and related works

2. Auctions market modeling with transaction fees and randomization

   2.1 The market characteristics

   2.2 Clearing Price rule

   2.3 Strategic Trader’s optimization and market quality

   2.4 Data and numerical analysis

   2.5 Strategic trader with full information: efficient but unfair market

   2.6 Imperfect information and inefficiency of auctions

3. Monitoring policies: transaction fees and clearing time randomization

   3.1 Bilevel optimization between the exchange and the strategic trader

   3.2 Randomization without fees

   3.3 Optimal transaction fees indexed on time to improve price impact for the trader

   3.4 Optimal transaction fees indexed on time: improving market quality while benefiting from the fees

4. Conclusions

A. Appendix: Numerical Methods

A.1 Problem of a Strategic Seller

A.2 Appendix: Problem of the Regulator

B Appendix: Illustrate Remark 2.4

References

1.2 Comparison and main flaws of limit order book

The literature to promote general market quality, discover better trading mechanisms, or improve market competition has been studied since the 60s; see [Garbade and Silber (1979)]. The continuous trading system has the advantage of providing ”immediate execution”. No one likes to wait; in [Kalay et al. (2002)], it is shown empirically that people prefer to trade in a continuous market instead of an auction market. However, such immediacy also creates a problem, especially after the emergence of high-frequency traders. [Budish et al. (2015)], [Wah and Wellman (2013)], and [Farmer and Skouras (2012)] question the efficiency of limit order mechanism rather than periodic auction. They study the efficiency of periodic auctions to monitor high-frequency trading advantages and increase market efficiency. [Budish et al. (2015)] compares two highly correlated stocks from real data and finds that the continuous trading system creates arbitrage opportunities in small time intervals. These arbitrage opportunities could be caught by high-frequency traders and thus incite competition in speed rather than price. High-frequency trading has brought down the execution time from several seconds at the start of the 2000s to microseconds nowadays. [Wah and Wellman (2013)] reaches a similar conclusion as they use simulations to show that high-frequency traders are latency arbitrageurs and widen the bid-ask spread. [Farmer and Skouras (2012)] discusses the negative impacts of high-frequency trading and proposes using periodic auctions (they also propose pro-rata rules with continuous market and randomized auction duration with periodic auctions).

Following these works, more studies focus on the advantages and disadvantages of continuous limit order books and periodic auctions. [Aquilina et al. (2022)] use exchange message data to quantify the speed competition in [Budish et al. (2015)]. However, restricting the competition in speed is only one of the characteristics of the periodic auction system compared to the continuous system. Recall that the other characteristic of a periodic auction differing from the CLOB is that the clearing price is set by combining the opinions of a batch of orders instead of just two. Such characteristics view market supply and demand more comprehensively and thus could improve the price discovery process. [Jusselin et al. (2021)] shows that optimally setting a clearing rule (price discovery and auction duration) for the periodic auction system enables the clearing price of most assets to be closer to the efficient prices compared to the continuous limit order book system. However, the continuous system could sometimes be optimal regarding the above mentioned price discovery process. [Graf et al. (2024)] shows by using real data that if we replace the continuous German Electricity Market with a frequent batch auction, there will be less traded volume but better price discovery (price is less noisy and closer to the fundamental value) and less liquidity cost measured in round-trip (CRT) cost. There are, of course, different opinions. In [Zhang and Ibikunle (2023)], they show empirically that subsecond frequent batch auction leads to a decline in adverse selection cost but an increase in relative spread and a decrease in information efficiency measured by ”autocorrelation of midpoint returns”. One thing to note about all these works is that researchers use different assumptions, models, and measures to reach their conclusions, so seemingly contrasting conclusions do not necessarily imply a contradiction.

Echoing the conclusion of [Jusselin et al. (2021)], “One size does not fit all”. Neither periodic auction nor continuous limit order book is the best by all measures and neither would benefit all affiliated groups. The interest of this paper is not to compare periodic auction and CLOB, but to study the possibility of a co-existence of the two systems. [Derchu et al. (2020)] proposes an Ad Hoc Electronic Auction Design (AHEAD) which allows traders to switch between continuous trading sessions and periodic trading sessions. They show that this design enables a less volatile clearing price and traders especially the smaller players benefit from this design compared to a continuous system or a periodic auction system.

In addition to the CLOB and the periodic auction market, there have been focuses and advances in other trading mechanisms. Dark pools differ from CLOB and auction in that orders are not displayed to the public; see [Ye (2011)], [Zhu (2014)], [Ye (2024)], [Baldacci et al. (2023)] for studies on whether a dark pool harm or help with market efficiency. See [Melton (2017)] for a latency floor design on CLOB to limit high frequency trading. Note also that cryptocurrency trading markets have interesting mechanism designs as well; see [Canidiom and Fritsch (2024)] for combining batch auction with automated market maker.

We also want to mention additionnal works as for example [Du and Zhu (2017)], [Brinkman and Wellman (2017)], [Fricke and Gerig (2018)], and [Jusselin et al. (2021)]. Each of these articles study the design of periodic auction to answer the following question: What is the optimal auction duration? [Wah et al. (2016)] uses simulation to show how fast and slow traders would choose between continuous market and periodic auction if the two markets run together; the model in this work does not consider strategic timing though. [Duffie and Zhu (2017)] proposes to add a size discovery market (”workup”) along with a batch auction market to increase allocation efficiency. A size discovery market allows traders to exchange inventory at a fixed-price so traders need not to worry about their price impact. The main differences between their model and ours are that they assume a strategic player in a batch auction submits a demand function instead of an order price or quantity and they focus on balancing the inventory level of each strategic player as they assume that a equal distribution of inventory among traders is the most desired. Despite the difference, their proposed design is worth to consider. Relating to [Duffie and Zhu (2017)]’s concern, [Goldberg and Tenorio (1997)] uses a Nash equilibrium model to show that strategic players in an auction lower demand and supply to avoid moving the clearing price away from their interests and such behavior could lead to a loss of trading volume in the market.