Optimal execution with liquidity risk in a diffusive order book market

Hyoeun Lee and Kiseop Lee ()
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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

International Journal of Financial Engineering (IJFE), 2023, vol. 10, issue 03, 1-32

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.

Keywords: Limit order book; optimal order placement problem; market order; liquidity cost; optimal execution problem (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S2424786323500184

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