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Optimal Auction Duration: A Price Formation Viewpoint

Author

Listed:
  • Jusselin Paul

    (École Polytechnique, Centre de Mathématiques Appliquées (CMAP), 91128 Palaiseau, France)

  • Mastrolia Thibaut

    (École Polytechnique, Centre de Mathématiques Appliquées (CMAP), 91128 Palaiseau, France)

  • Rosenbaum Mathieu

    (École Polytechnique, Centre de Mathématiques Appliquées (CMAP), 91128 Palaiseau, France)

Abstract

We consider an auction market in which market makers fill the order book during a given time period while some other investors send market orders. We define the clearing price of the auction as the price maximizing the exchanged volume at the clearing time according to the supply and demand of each market participant. Then we derive in a semiexplicit form the error made between this clearing price and the efficient price as a function of the auction duration. We study the impact of the behavior of market takers on this error. To do so, we consider the case of naive market takers and that of rational market takers playing a Nash equilibrium to minimize their transaction costs. We compute the optimal duration of the auctions for 77 stocks traded on Euronext and compare the quality of the price formation process under this optimal value to the case of a continuous limit order book. Continuous limit order books are found to be usually suboptimal. However, in terms of our metric, they only moderately impair the quality of the price formation process. The order of magnitude of optimal auction durations is from 2–10 minutes.

Suggested Citation

  • Jusselin Paul & Mastrolia Thibaut & Rosenbaum Mathieu, 2021. "Optimal Auction Duration: A Price Formation Viewpoint," Operations Research, INFORMS, vol. 69(6), pages 1734-1745, November.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:6:p:1734-1745
    DOI: 10.1287/opre.2021.2113
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