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Optimal execution with liquidity risk in a diffusive order book market

Author

Listed:
  • Hyoeun Lee

    (Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, USA)

  • Kiseop Lee

    (Department of Statistics, Purdue University, West Lafayette, IN, USA)

Abstract

We study the optimal order placement strategy with the presence of a liquidity cost. In this problem, a stock trader wishes to clear her large inventory by a predetermined time horizon T. A trader uses both limit and market orders, and a large market order faces an adverse price movement caused by the liquidity risk. First, we study a single period model where the trader places a limit order and/or a market order at the beginning. We show the behavior of optimal amount of market order, m*, and optimal placement of limit order, y*, under different market conditions. Next, we extend it to a multi-period model, where the trader makes sequential decisions of limit and market orders at multiple time points.

Suggested Citation

  • Hyoeun Lee & Kiseop Lee, 2023. "Optimal execution with liquidity risk in a diffusive order book market," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(03), pages 1-32, September.
    • Handle: RePEc:wsi:ijfexx:v:10:y:2023:i:03:n:s2424786323500184
    DOI: 10.1142/S2424786323500184
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