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Hedging of covered options with linear market impact and gamma constraint

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  • B Bouchard

    (CEREMADE)

  • G Loeper

    (FiQuant)

  • Y Zou

    (CEREMADE)

Abstract

Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the super-replication price is the viscosity solution of a fully non-linear parabolic equation. As a by-product, we show how $\epsilon$-optimal strategies can be constructed. Finally, a numerical resolution scheme is proposed.

Suggested Citation

  • B Bouchard & G Loeper & Y Zou, 2015. "Hedging of covered options with linear market impact and gamma constraint," Papers 1512.07087, arXiv.org.
    • Handle: RePEc:arx:papers:1512.07087
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    References listed on IDEAS

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    1. 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..
    2. Soner, H. Mete & Cetin, Umut & Touzi, Nizar, 2010. "Option hedging for small investors under liquidity costs," LSE Research Online Documents on Economics 28992, London School of Economics and Political Science, LSE Library.
    3. Umut Çetin & H. Soner & Nizar Touzi, 2010. "Option hedging for small investors under liquidity costs," Finance and Stochastics, Springer, vol. 14(3), pages 317-341, September.
    4. B Bouchard & G Loeper & Y Zou, 2015. "Almost-sure hedging with permanent price impact," Working Papers hal-01133223, HAL.
    5. B. Bouchard & G. Loeper & Y. Zou, 2015. "Almost-sure hedging with permanent price impact," Papers 1503.05475, arXiv.org.
    6. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    7. Liu, Hong & Yong, Jiongmin, 2005. "Option pricing with an illiquid underlying asset market," Journal of Economic Dynamics and Control, Elsevier, vol. 29(12), pages 2125-2156, December.
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