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Optimal execution strategy in liquidity framework

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  • Chiara Benazzoli
  • Luca Di Persio

Abstract

A trader wishes to execute a given number of shares of an illiquid asset. Since the asset price also depends on the trading behaviour, the trader main aim is to find the execution strategy that minimizes the related expected costs. We solve this problem in a discrete time framework, by modeling the asset price dynamic as an arithmetic random walk with drift and volatility both modeled as Markov stochastic processes. The market impact is assumed to follow a Markov process. We found the unique execution strategy minimizing the implementation shortfall when short selling is allowed. This optimal strategy is given as solution of a forward-backward system of stochastic equations depending on conditional expectations of future values of model parameters. In the opposite case, namely when short selling is prohibited, we numerically obtain the solution for the associated Bellman equation that an optimal trading strategy must satisfy.

Suggested Citation

  • Chiara Benazzoli & Luca Di Persio, 2017. "Optimal execution strategy in liquidity framework," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1364902-136, January.
    • Handle: RePEc:taf:oaefxx:v:5:y:2017:i:1:p:1364902
    DOI: 10.1080/23322039.2017.1364902
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    References listed on IDEAS

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    1. Ku, Hyejin & Lee, Kiseop & Zhu, Huaiping, 2012. "Discrete time hedging with liquidity risk," Finance Research Letters, Elsevier, vol. 9(3), pages 135-143.
    2. Alexander Schied, 2013. "Robust Strategies for Optimal Order Execution in the Almgren--Chriss Framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(3), pages 264-286, July.
    3. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29, January.
    4. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    5. Alexander Schied, 2012. "Robust Strategies for Optimal Order Execution in the Almgren-Chriss Framework," Papers 1204.2717, arXiv.org, revised May 2013.
    6. Patrick Cheridito & Tardu Sepin, 2014. "Optimal Trade Execution Under Stochastic Volatility and Liquidity," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(4), pages 342-362, September.
    7. Damiano Brigo & Giuseppe Di Graziano, 2014. "Optimal trade execution under displaced diffusions dynamics across different risk criteria," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 1-17.
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