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American options with gradual exercise under proportional transaction costs

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  • Alet Roux
  • Tomasz Zastawniak

Abstract

American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomised) stopping time. The introduction of gradual exercise leads to tighter bounds on the option price when compared to the case studied in the existing literature, where the standard assumption is that the option can only be exercised instantly at an ordinary stopping time. Algorithmic constructions for the bid and ask prices and the associated superhedging strategies and optimal mixed stoping times for an American option with gradual exercise are developed and implemented, and dual representations are established.

Suggested Citation

  • Alet Roux & Tomasz Zastawniak, 2013. "American options with gradual exercise under proportional transaction costs," Papers 1308.2688, arXiv.org.
    • Handle: RePEc:arx:papers:1308.2688
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    References listed on IDEAS

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    1. Bruno Bouchard & Emmanuel Temam, 2005. "On the Hedging of American Options in Discrete Time Markets with Proportional Transaction Costs," Papers math/0502189, arXiv.org.
    2. repec:dau:papers:123456789/1805 is not listed on IDEAS
    3. 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.
    4. 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.
    5. Andreas Lohne & Birgit Rudloff, 2011. "An algorithm for calculating the set of superhedging portfolios in markets with transaction costs," Papers 1107.5720, arXiv.org, revised Dec 2013.
    6. 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.
    7. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    8. Alet Roux & Tomasz Zastawniak, 2011. "American and Bermudan options in currency markets under proportional transaction costs," Papers 1108.1910, arXiv.org, revised Jun 2014.
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