American options with gradual exercise under proportional transaction costs
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.
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- 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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- Temam, Emmanuel & Bouchard, Bruno, 2005. "On the Hedging of American Options in Discrete Time Markets with Proportional Transaction Costs," Economics Papers from University Paris Dauphine 123456789/1805, Paris Dauphine University.
- 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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