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Superreplication when trading at market indifference prices

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  • Peter Bank
  • Selim Gokay

Abstract

We study superreplication of European contingent claims in discrete time in a large trader model with market indifference prices recently proposed by Bank and Kramkov. We introduce a suitable notion of efficient friction in this framework, adopting a terminology introduced by Kabanov, Rasonyi, and Stricker in the context of models with proportional transaction costs. In our framework, efficient friction ensures that large positions of the investor may lead to large losses, a fact from which we derive the existence of superreplicating strategies. We illustrate that without this condition there may be no superreplicating strategy with minimal costs. In our main result, we establish efficient friction under a tail condition on the conditional distributions of the traded securities and under an asymptotic criterion on risk aversions of the market makers. Another result asserts that strict monotonicity of the conditional essential infima and suprema of the security prices is sufficient for efficient friction. We give examples that satisfy the assumptions in our conditions, which include non-degenerate finite sample space models as well as Levy processes and an affine stochastic volatility model of Barndorff-Nielsen-Shepard type.

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  • Peter Bank & Selim Gokay, 2013. "Superreplication when trading at market indifference prices," Papers 1310.3113, arXiv.org.
  • Handle: RePEc:arx:papers:1310.3113
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    References listed on IDEAS

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    1. (**), Christophe Stricker & (*), Miklós Rásonyi & Yuri Kabanov, 2002. "No-arbitrage criteria for financial markets with efficient friction," Finance and Stochastics, Springer, vol. 6(3), pages 371-382.
    2. repec:dau:papers:123456789/5647 is not listed on IDEAS
    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. Luciano Campi & Walter Schachermayer, 2006. "A super-replication theorem in Kabanov’s model of transaction costs," Finance and Stochastics, Springer, vol. 10(4), pages 579-596, December.
    5. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
    6. 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..
    7. 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.
    8. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466.
    9. Dylan Possamai & Nizar Touzi & H. Mete Soner, 2012. "Large liquidity expansion of super-hedging costs," Papers 1208.3785, arXiv.org, revised Apr 2015.
    10. repec:dau:papers:123456789/5526 is not listed on IDEAS
    11. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    12. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232.
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