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Option pricing and hedging with execution costs and market impact

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  • Olivier Gu'eant
  • Jiang Pu

Abstract

This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in a frictionless market, traders cannot be perfectly hedged because of execution costs and market impact. They indeed face a trade-off between hedging errors and costs that can be solved by using stochastic optimal control. Our modelling framework, which is inspired by the recent literature on optimal execution, makes it possible to account for both execution costs and the lasting market impact of trades. Prices are obtained through the indifference pricing approach. Numerical examples are provided, along with comparisons to standard methods.

Suggested Citation

  • Olivier Gu'eant & Jiang Pu, 2013. "Option pricing and hedging with execution costs and market impact," Papers 1311.4342, arXiv.org, revised Apr 2015.
    • Handle: RePEc:arx:papers:1311.4342
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    References listed on IDEAS

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    4. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Ibrahim Ekren & Johannes Muhle-Karbe, 2017. "Portfolio Choice with Small Temporary and Transient Price Impact," Papers 1705.00672, arXiv.org, revised Apr 2020.
    2. Masaaki Fukasawa & Mitja Stadje, 2017. "Perfect hedging under endogenous permanent market impacts," Papers 1702.01385, arXiv.org.
    3. Peter Bank & Mete Soner & Moritz Vo{ss}, 2015. "Hedging with Temporary Price Impact," Papers 1510.03223, arXiv.org, revised Jul 2016.
    4. Qing-Qing Yang & Wai-Ki Ching & Jiawen Gu & Tak-Kuen Siu, 2020. "Trading strategy with stochastic volatility in a limit order book market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 277-301, June.
    5. Anderegg, Benjamin & Ulmann, Florian & Sornette, Didier, 2022. "The impact of option hedging on the spot market volatility," Journal of International Money and Finance, Elsevier, vol. 124(C).
    6. Olivier Gu'eant, 2014. "Optimal execution of ASR contracts with fixed notional," Papers 1410.1481, arXiv.org, revised May 2016.

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