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Price impact equilibrium with transaction costs and TWAP trading

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Abstract

We prove the existence of an equilibrium in a model with transaction costs and price impact where two agents are incentivized to trade towards a target. The two types of frictions—price impact and transaction costs—lead the agents to two distinct changes in their optimal investment approach: price impact causes agents to continuously trade in smaller amounts, while transaction costs cause the agents to cease trading before the end of the trading period. As the agents lose wealth because of transaction costs, the exchange makes a profit. We prove the existence of a strictly positive optimal transaction cost from the exchange’s perspective.

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Notes

  1. Even in the case of a longer time horizon, Hartzmark and Solomon [15], Boudoukh et al. [6], and Atmaz and Basak [3] make the case that the non-dividend paying stocks are prevalent in the stock market and potentially play a prominent role in longer-time horizon asset pricing models.

  2. We restrict strategies to those with finite variation since strategies with infinite first-order variation would result in infinite transaction costs.

  3. We would like to thank Jetlir Duraj for discussions on this issue.

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Authors and Affiliations

  1. Department of Mathematics, Florida State University, Tallahassee, USA

    Eunjung Noh

  2. Department of Mathematics, Rutgers University, New Brunswick, USA

    Kim Weston

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  1. Eunjung Noh
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  2. Kim Weston
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Correspondence to Kim Weston.

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K. Weston: The authors would like to thank Xiao Chen, Jetlir Duraj, and Kasper Larsen for helpful discussions on this work. We would also like to thank the anonymous referees and associate editor for their comments, which greatly improved the paper. The second author acknowledges support by the National Science Foundation under Grant No. DMS#1908255 (2019–2022) and DMS#1606253 (2016–2020). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF)

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Noh, E., Weston, K. Price impact equilibrium with transaction costs and TWAP trading. Math Finan Econ 16, 187–204 (2022). https://doi.org/10.1007/s11579-021-00306-0

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