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Trading co‐integrated assets with price impact

Author

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  • Álvaro Cartea
  • Luhui Gan
  • Sebastian Jaimungal

Abstract

Executing a basket of co‐integrated assets is an important task facing investors. Here, we show how to do this accounting for the informational advantage gained from assets within and outside the basket, as well as for the permanent price impact of market orders (MOs) from all market participants, and the temporary impact that the agent's MOs have on prices. The execution problem is posed as an optimal stochastic control problem and we demonstrate that, under some mild conditions, the value function admits a closed‐form solution, and prove a verification theorem. Furthermore, we use data of five stocks traded in the Nasdaq exchange to estimate the model parameters and use simulations to illustrate the performance of the strategy. As an example, the agent liquidates a portfolio consisting of shares in Intel Corporation and Market Vectors Semiconductor ETF. We show that including the information provided by three additional assets (FARO Technologies, NetApp, Oracle Corporation) considerably improves the strategy's performance; for the portfolio we execute, it outperforms the multiasset version of Almgren–Chriss by approximately 4–4.5 basis points.

Suggested Citation

  • Álvaro Cartea & Luhui Gan & Sebastian Jaimungal, 2019. "Trading co‐integrated assets with price impact," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 542-567, April.
    • Handle: RePEc:bla:mathfi:v:29:y:2019:i:2:p:542-567
    DOI: 10.1111/mafi.12181
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    Cited by:

    1. Fayc{c}al Drissi, 2022. "Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals," Papers 2202.07478, arXiv.org, revised Aug 2023.
    2. Philippe Bergault & Fayc{c}al Drissi & Olivier Gu'eant, 2021. "Multi-asset optimal execution and statistical arbitrage strategies under Ornstein-Uhlenbeck dynamics," Papers 2103.13773, arXiv.org, revised Mar 2022.
    3. Masamitsu Ohnishi & Makoto Shimoshimizu, 2024. "Trade execution games in a Markovian environment," Papers 2405.07184, arXiv.org.
    4. Yi Li & Ju’e Guo & Kin Keung Lai & Jinzhao Shi, 2022. "Optimal portfolio liquidation with cross-price impacts on trading," Operational Research, Springer, vol. 22(2), pages 1083-1102, April.
    5. Masamitsu Ohnishi & Makoto Shimoshimizu, 2022. "Optimal Pair–Trade Execution with Generalized Cross–Impact," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 253-289, June.

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