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Optimal Execution with Quadratic Variation Inventories

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  • Rene Carmona
  • Laura Leal

Abstract

The first half of the paper is devoted to description and implementation of statistical tests arguing for the presence of a Brownian component in the inventories and wealth processes of individual traders. We use intra-day data from the Toronto Stock Exchange to provide empirical evidence of this claim. We work with regularly spaced time intervals, as well as with asynchronously observed data. The tests reveal with high significance the presence of a non-zero Brownian motion component. The second half of the paper is concerned with the analysis of trader behaviors throughout the day. We extend the theoretical analysis of an existing optimal execution model to accommodate the presence of It\^o inventory processes, and we compare empirically the optimal behavior of traders in such fitted models, to their actual behavior as inferred from the data.

Suggested Citation

  • Rene Carmona & Laura Leal, 2021. "Optimal Execution with Quadratic Variation Inventories," Papers 2104.14615, arXiv.org.
    • Handle: RePEc:arx:papers:2104.14615
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    References listed on IDEAS

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    1. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2011. "A Functional Filtering and Neighborhood Truncation Approach to Integrated Quarticity Estimation," NBER Working Papers 17152, National Bureau of Economic Research, Inc.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    3. Per Mykland, 2012. "A Gaussian calculus for inference from high frequency data," Annals of Finance, Springer, vol. 8(2), pages 235-258, May.
    4. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
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    Cited by:

    1. René Carmona & Claire Zeng, 2022. "Optimal Execution with Identity Optionality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 29(4), pages 261-287, July.
    2. Ren'e Carmona & Mathieu Lauri`ere, 2021. "Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance," Papers 2107.04568, arXiv.org.

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