Authors:
(1) Thibaut Mastrolia, UC Berkeley, Department of Industrial Engineering and Operations Research (thibaut.mastrolia@berkeley.edu);
(2) Tianrui Xu, UC Berkeley, Department of Mathematics (tianrui.xu@berkeley.edu). Authors: Authors: (1) Thibaut Mastrolia, UC Berkeley, Department of Industrial Engineering and Operations Research (thibaut.mastrolia@berkeley.edu); (2) Tianrui Xu, UC Berkeley, Department of Mathematics (tianrui.xu@berkeley.edu). Table of Links Abstract Abstract Abstract 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


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


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


Conclusions 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 Introduction Introduction 1.1 Periodic auction and continuous limit order book 1.1 Periodic auction and continuous limit order book 1.2 Comparison and main flaws of 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 1.3 Optimal policies to cure auction’s inefficiencies and related works 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 Auctions market modeling with transaction fees and randomization Auctions market modeling with transaction fees and randomization 2.1 The market characteristics 2.1 The market characteristics 2.2 Clearing Price rule 2.2 Clearing Price rule 2.3 Strategic Trader’s optimization and market quality 2.3 Strategic Trader’s optimization and market quality 2.4 Data and numerical analysis 2.4 Data and numerical analysis 2.5 Strategic trader with full information: efficient but unfair market 2.5 Strategic trader with full information: efficient but unfair market 2.6 Imperfect information and inefficiency of auctions 2.6 Imperfect information and inefficiency of auctions 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 Monitoring policies: transaction fees and clearing time randomization Monitoring policies: transaction fees and clearing time randomization 3.1 Bilevel optimization between the exchange and the strategic trader 3.1 Bilevel optimization between the exchange and the strategic trader 3.2 Randomization without fees 3.2 Randomization without fees 3.3 Optimal transaction fees indexed on time to improve price impact for the trader 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 3.4 Optimal transaction fees indexed on time: improving market quality while benefiting from the fees Conclusions Conclusions Conclusions Conclusions A. Appendix: Numerical Methods A. Appendix: Numerical Methods A.1 Problem of a Strategic Seller A.1 Problem of a Strategic Seller A.2 Appendix: Problem of the Regulator A.2 Appendix: Problem of the Regulator B Appendix: Illustrate Remark 2.4 B Appendix: Illustrate Remark 2.4 References References Abstract Flaws of a continuous limit order book mechanism raise the question of whether a continuous trading session and a periodic auction session would bring better efficiency. This paper wants to go further in designing a periodic auction when both a continuous market and a periodic auction market are available to traders. In a periodic auction, we discover that a strategic trader could take advantage of the accumulated information available along the auction duration by arriving at the latest moment before the auction closes, increasing the price impact on the market. Such price impact moves the clearing price away from the efficient price and may disturb the efficiency of a periodic auction market. We thus propose and quantify the effect of two remedies to mitigate these flaws: randomizing the auction’s closing time and optimally designing a transaction fees policy. Our results show that these policies encourage a strategic trader to send their orders earlier to enhance the efficiency of the auction market, illustrated by data extracted from Alphabet and Apple stocks. 1.1 Periodic auction and continuous limit order book Continuous limit order book (CLOB for short or continuous double auction) and periodic auction (also called batch auction or call auction) are the two most commonly used electronic trading systems around the world. For example, New York Stock Exchange, NASDAQ (U.S.), London Stock Exchange all use the continuous limit order book system during normal trading hours and switch to a periodic auction system for the opening and closing auctions to determine the open price and the closing price of each trading day. CBOE Europe have both continuous limit order book and periodic auction open during the normal trading hours. CowSwap a cryptocurrency exchange uses periodic auction to settle orders. The trading mechanisms of the two systems are as follows. A continuous limit order book market executes incoming orders continuously, i.e., when there is a matching order between a market order and a limit order. Every matched order trades at a price that depends on its requested price and the price of the limit order it is matched to. In comparison, a periodic auction market executes incoming orders as a batch and applies a uniform price to all executed orders in this batch after a specific time horizon. To be more specific, a market order would initiate an auction that would be open for a specific time interval until a terminal time, which is called the clearing time. During the auction, the exchange receives orders from market participants. Market participants give the exchange a proposed price at which they are willing to buy or sell the asset and a specific volume. When the auction closes, the exchange determines a clearing price by setting it to maximize the number of fulfilled orders (or to minimize the imbalance). Every order may be executed at the clearing price instead of their proposed price. Due to this rule, limit buying orders with a proposed price below the clearing price and limit selling orders with a proposed price above the clearing price would not be executed. Despite the difference between the two trading systems, a continuous limit order book can be considered a periodic auction whose duration equals 0 second, see for example [Jusselin et al. (2021)]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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