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On the Hedging of American Options in Discrete Time Markets with Proportional Transaction Costs

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  • Bruno Bouchard

    (PMA)

  • Emmanuel Temam

    (PMA)

Abstract

In this note, we consider a general discrete time financial market with proportional transaction costs as in Kabanov and Stricker (2001), Kabanov et al. (2002), Kabanov et al. (2003) and Schachermayer (2004). We provide a dual formulation for the set of initial endowments which allow to super-hedge some American claim. We show that this extends the result of Chalasani and Jha (2001) which was obtained in a model with constant transaction costs and risky assets which evolve on a finite dimensional tree. We also provide fairly general conditions under which the expected formulation in terms of stopping times does not work.

Suggested Citation

  • Bruno Bouchard & Emmanuel Temam, 2005. "On the Hedging of American Options in Discrete Time Markets with Proportional Transaction Costs," Papers math/0502189, arXiv.org.
    • Handle: RePEc:arx:papers:math/0502189
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    References listed on IDEAS

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    1. 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.
    2. Prasad Chalasani & Somesh Jha, 2001. "Randomized Stopping Times and American Option Pricing with Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 33-77, January.
    3. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
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    Cited by:

    1. Johannes Gerer & Gregor Dorfleitner, 2018. "Optimal discrete hedging of American options using an integrated approach to options with complex embedded decisions," Review of Derivatives Research, Springer, vol. 21(2), pages 175-199, July.
    2. Tokarz, Krzysztof & Zastawniak, Tomasz, 2006. "American contingent claims under small proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 65-85, December.
    3. Alet Roux & Tomasz Zastawniak, 2013. "American options with gradual exercise under proportional transaction costs," Papers 1308.2688, arXiv.org.
    4. Alet Roux & Tomasz Zastawniak, 2016. "Game options with gradual exercise and cancellation under proportional transaction costs," Papers 1612.02312, arXiv.org.
    5. Mun-Chol Kim & Song-Chol Ryom, 2022. "Pathwise superhedging under proportional transaction costs," Mathematics and Financial Economics, Springer, volume 16, number 4, September.
    6. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    7. Denis Belomestny & Volker Krätschmer, 2017. "Optimal Stopping Under Probability Distortions," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 806-833, August.
    8. Yuri Kifer, 2012. "Hedging of game options in discrete markets with transaction costs," Papers 1206.4506, arXiv.org.
    9. M. Pınar & A. Camcı, 2012. "An Integer Programming Model for Pricing American Contingent Claims under Transaction Costs," Computational Economics, Springer;Society for Computational Economics, vol. 39(1), pages 1-12, January.
    10. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.

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