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Explicit characterization of the super-replication strategy in financial markets with partial transaction costs

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  • Imen Bentahar
  • Bruno Bouchard

Abstract

We consider a continuous time multivariate financial market with proportional transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in Bouchard and Touzi (2000) except that some of the assets can be exchanged freely, i.e. without paying transaction costs. This is the so-called non-effcient friction case. To our knowledge, this is the first time that such a model is considered in a continuous time setting. In this context, we generalize the result of the above paper and prove that the super-replication price is given by the cost of the cheapest hedging strategy in which the number of non-freely exchangeable assets is kept constant over time.

Suggested Citation

  • Imen Bentahar & Bruno Bouchard, 2005. "Explicit characterization of the super-replication strategy in financial markets with partial transaction costs," SFB 649 Discussion Papers SFB649DP2005-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2005-053
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    References listed on IDEAS

    as
    1. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    2. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    3. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
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    7. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    8. Nizar Touzi, 1999. "Super-replication under proportional transaction costs: From discrete to continuous-time models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 297-320, October.
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    More about this item

    Keywords

    Transaction costs; hedging options; viscosity solutions;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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