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Option pricing with market impact and non-linear Black and Scholes pde's

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  • Gregoire Loeper
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    Abstract

    We propose a few variations around a simple model in order to take into account the market impact of the option seller when hedging an option. This "retro-action" mechanism turns the linear Black and Scholes PDE into a non-linear one. This model allows also to retrieve some earlier results of \cite{CheriSonTouz}. Numerical simulations are then performed.

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    File URL: http://arxiv.org/pdf/1301.6252
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1301.6252.

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    Date of creation: Jan 2013
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    Handle: RePEc:arx:papers:1301.6252

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    Web page: http://arxiv.org/

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    1. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
    2. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
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    Cited by:
    1. Frédéric Abergel & Grégoire Loeper, 2013. "Pricing and hedging contingent claims with liquidity costs and market impact," Working Papers hal-00802402, HAL.

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