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Optimal execution and speculation with trade signals

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  • Peter Bank
  • 'Alvaro Cartea
  • Laura Korber

Abstract

We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity process which reflects the balance of the demand and supply of liquidity. Limit and market orders mutually excite each other so that liquidity is mean reverting. We use the theory of Meyer-$\sigma$-fields to introduce a short-term signal process from which a trader learns about imminent changes in order flow. In this setting, we examine an optimal execution problem and derive the Hamilton--Jacobi--Bellman (HJB) equation for the value function. The HJB equation is solved numerically and we illustrate how the trader uses the signal to enhance the performance of execution problems and to execute speculative strategies.

Suggested Citation

  • Peter Bank & 'Alvaro Cartea & Laura Korber, 2023. "Optimal execution and speculation with trade signals," Papers 2306.00621, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:2306.00621
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    References listed on IDEAS

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    1. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
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    8. Peter Bank & David Besslich, 2018. "Modelling information flows by Meyer-$\sigma$-fields in the singular stochastic control problem of irreversible investment," Papers 1810.08495, arXiv.org, revised Mar 2020.
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