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Optimal execution and block trade pricing: a general framework

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  • Olivier Guéant

    (LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this article, we develop a general CARA framework to study optimal execution and to price block trades. We prove existence and regularity results for optimal liquidation strategies and we provide several differential characterizations. We also give two different proofs that the usual restriction to deterministic liquidation strategies is optimal. In addition, we focus on the important topic of block trade pricing and we therefore give a price to financial (il)liquidity. In particular, we provide a closed-form formula for the price a block trade when there is no time constraint to liquidate, and a differential characterization in the time-constrained case.

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  • Olivier Guéant, 2015. "Optimal execution and block trade pricing: a general framework," Post-Print hal-01393118, HAL.
    • Handle: RePEc:hal:journl:hal-01393118
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    Cited by:

    1. Alexis Bismuth & Olivier Gu'eant & Jiang Pu, 2016. "Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty," Papers 1611.07843, arXiv.org, revised Mar 2019.
    2. Olivier Guéant & Jiang Pu, 2017. "Option Pricing And Hedging With Execution Costs And Market Impact," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 803-831, July.
    3. Ulrich Horst & Evgueni Kivman, 2024. "Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies," Finance and Stochastics, Springer, vol. 28(3), pages 759-812, July.
    4. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.

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