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Large liquidity expansion of super-hedging costs

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  • Dylan Possamai
  • Nizar Touzi
  • H. Mete Soner
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    Abstract

    We consider a financial market with liquidity cost as in \c{C}etin, Jarrow and Protter [2004], where the supply function S{\epsilon}(s,{\nu}) depends on a parameter {\epsilon}\geq0 with S0(s,{\nu})=s corresponding to the perfect liquid situation. Using the PDE characterization of \c{C}etin, Soner and Touzi [2010], of the super-hedging cost of an option written on such a stock, we provide a Taylor expansion of the super-hedging cost in powers of {\epsilon}. In particular, we explicitly compute the first term in the expansion for a European Call option and give bounds for the order of the expansion for a European Digital Option.

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    File URL: http://arxiv.org/pdf/1208.3785
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1208.3785.

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    Date of creation: Aug 2012
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    Publication status: Published in Asymptotic Analysis, 79(1-2), 2012, 45-64
    Handle: RePEc:arx:papers:1208.3785

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    Web page: http://arxiv.org/

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    References

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    1. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29.
    2. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    3. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
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    Cited by:
    1. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2013. "Hedging under an expected loss constraint with small transaction costs," Papers 1309.4916, arXiv.org.
    2. Peter Bank & Selim G\"okay, 2013. "Superreplication when trading at market indifference prices," Papers 1310.3113, arXiv.org.

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