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Option hedging for small investors under liquidity costs

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  • Soner, H. Mete
  • Cetin, Umut
  • Touzi, Nizar

Abstract

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).

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:28992
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    File URL: http://eprints.lse.ac.uk/28992/
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    References listed on IDEAS

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    More about this item

    Keywords

    stochastic target problems; differential-equations; portfolio constraints; viscosity solutions; gamma-constraints; super-replication; pricing theory; markets; ISI;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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