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Almost-sure hedging with permanent price impact

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  • B. Bouchard
  • G. Loeper
  • Y. Zou

Abstract

We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in the sense of viscosity solutions. When it admits a smooth solution, it provides a perfect hedging strategy.

Suggested Citation

  • B. Bouchard & G. Loeper & Y. Zou, 2015. "Almost-sure hedging with permanent price impact," Papers 1503.05475, arXiv.org.
    • Handle: RePEc:arx:papers:1503.05475
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    File URL: http://arxiv.org/pdf/1503.05475
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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. H. Mete Soner & Nizar Touzi, 2007. "Hedging Under Gamma Constraints By Optimal Stopping And Face‐Lifting," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 59-79, January.
    4. 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.
    5. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    6. 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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    Cited by:

    1. B Bouchard & G Loeper & Y Zou, 2015. "Hedging of covered options with linear market impact and gamma constraint," Papers 1512.07087, arXiv.org.
    2. B Bouchard & G Loeper & Y Zou, 2015. "Hedging of covered options with linear market impact and gamma constraint," Working Papers hal-01247523, HAL.
    3. Bruno Bouchard & G. Loeper & Y. Zou, 2017. "Hedging of covered options with linear market impact and gamma constraint," Post-Print hal-01611790, HAL.
    4. Dirk Becherer & Todor Bilarev & Peter Frentrup, 2017. "Stability for gains from large investors' strategies in M1/J1 topologies," Papers 1701.02167, arXiv.org, revised Mar 2018.
    5. Bruno Bouchard & G Loeper & Y Zou, 2017. "Hedging of covered options with linear market impact and gamma constraint," Post-Print hal-01247523, HAL.
    6. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.

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