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Optimal trade execution under displaced diffusions dynamics across different risk criteria

Author

Listed:
  • Damiano Brigo

    (Department of Mathematics, Imperial College London, UK;
    Capco Research Institute, UK)

  • Giuseppe Di Graziano

    (Department of Mathematics, Imperial College London, UK;
    Deutsche Bank AG, London, UK)

Abstract

We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion (DD). Optimal strategies in the adapted class under various risk criteria, namely value-at-risk (VaR), expected shortfall (ES) and a new criterion called squared asset expectation (SAE), related to a version of the cost variance measure, are derived and compared. It is well known that DDs exhibit dynamics that are in-between arithmetic Brownian motions (ABM) and geometric Brownian motions (GBM) depending of the choice of the shift parameter. Furthermore, DD allows for changes in the support of the mid asset price distribution, allowing one to include a minimum permitted value for the mid price, either positive or negative. We study the dependence of the optimal solution on the choice of the risk aversion criterion. Optimal solutions across criteria and asset dynamics are comparable although differences are not negligible for high levels of risk aversion and low market impact assets. This is illustrated with numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:jfexxx:v:01:y:2014:i:02:n:s2345768614500184
    DOI: 10.1142/S2345768614500184
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    Citations

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    Cited by:

    1. Claudio Bellani & Damiano Brigo, 2021. "Mechanics of good trade execution in the framework of linear temporary market impact," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 143-163, January.
    2. Damiano Brigo & Clement Piat, 2016. "Static vs adapted optimal execution strategies in two benchmark trading models," Papers 1609.05523, arXiv.org.
    3. M. Alessandra Crisafi & Andrea Macrina, 2016. "Simultaneous Trading In ‘Lit’ And Dark Pools," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-33, December.
    4. 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.
    5. Masashi Ieda, 2015. "A dynamic optimal execution strategy under stochastic price recovery," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-24, December.
    6. Masashi Ieda, 2015. "A dynamic optimal execution strategy under stochastic price recovery," Papers 1502.04521, arXiv.org.

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