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Option hedging for small investors under liquidity costs

  • H. Mete Soner
  • Umut Cetin
  • Nizar Touzi
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    Following the framework of Cetin et al. (finance stoch. 8:311-341, 2004), we study the problem of super-replication in the presence of liquidity costs under additional restrictions on the gamma of the hedging strategies in a generalized black-scholes economy. We find that the minimal super-replication price is different from the one suggested by the black-scholes formula and is the unique viscosity solution of the associated dynamic programming equation. This is in contrast with the results of Cetin et al. (Finance Stoch. 8:311-341, 2004), who find that the arbitrage-free price of a contingent claim coincides with the Black-Scholes price. However, in Cetin et al. (Finance Stoch. 8:311-341, 2004) a larger class of admissible portfolio processes is used, and the replication is achieved in the L (2) approximating sense. JEL (C61 - G13 - D52).

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    File URL: http://eprints.lse.ac.uk/28992/
    File Function: Open access version.
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    Paper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 28992.

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    Date of creation: 2010
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    Publication status: Published in Finance and Stochastics, 2010, 14(3), pp. 317-341. ISSN: 0949-2984
    Handle: RePEc:ehl:lserod:28992
    Contact details of provider: Postal: LSE Library Portugal Street London, WC2A 2HD, U.K.
    Phone: +44 (020) 7405 7686
    Web page: http://www.lse.ac.uk/

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    1. 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.
    2. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
    3. 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.
    4. U. �etin & R. Jarrow & P. Protter & M. Warachka, 2006. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," Review of Financial Studies, Society for Financial Studies, vol. 19(2), pages 493-529.
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