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The British Lookback Option with Fixed Strike

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  • Yerkin Kitapbayev

Abstract

We continue research of the new type of options called 'British' that was introduced recently by presenting the British lookback option with fixed strike. This article generalizes the work about the British Russian option and provides financial analysis of lookback options with fixed non-zero strike. The British holder enjoys the early exercise feature of American options whereupon his pay-off (deliverable immediately) is the 'best prediction' of the European lookback pay-off under the hypothesis that the true drift of the stock price equals a contract drift. We derive a closed-form expression for the arbitrage-free price in terms of the optimal stopping boundary of two-dimensional optimal stopping problem with a scaling strike and show that the rational exercise boundary of the option can be characterized via the unique solution to a nonlinear integral equation. We also show the remarkable numerical example where the rational exercise boundary exhibits a discontinuity. Using these results, we perform a financial analysis of the British lookback option with fixed strike, which shows that with the contract drift properly selected this instrument not only provides an effective protection mechanism, but becomes a very attractive alternative to the classic European/American lookback option from speculator's point of view and gives high returns when stock movements are favourable.

Suggested Citation

  • Yerkin Kitapbayev, 2015. "The British Lookback Option with Fixed Strike," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 238-260, July.
    • Handle: RePEc:taf:apmtfi:v:22:y:2015:i:3:p:238-260
    DOI: 10.1080/1350486X.2015.1019156
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    References listed on IDEAS

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    1. Kristoffer Glover & Goran Peskir & Farman Samee, 2010. "The British Russian Option," Research Paper Series 269, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Goran Peskir & Farman Samee, 2013. "The British call option," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 95-109, January.
    3. Goran Peskir & Farman Samee, 2011. "The British Put Option," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(6), pages 537-563, April.
    4. Pavel V. Gapeev, 2006. "Discounted Optimal Stopping for Maxima of some Jump-Diffusion Processes," SFB 649 Discussion Papers SFB649DP2006-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Kristoffer Glover & Goran Peskir & Farman Samee, 2009. "The British Asian Option," Research Paper Series 249, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
    7. Pavel V. Gapeev, 2006. "Discounted Optimal Stopping for Maxima in Diffusion Models with Finite Horizon," SFB 649 Discussion Papers SFB649DP2006-057, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Goran Peskir, 2005. "The Russian option: Finite horizon," Finance and Stochastics, Springer, vol. 9(2), pages 251-267, April.
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    1. Min Gao, 2017. "The British Asset-Or-Nothing Put Option," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-19, June.
    2. Damir Filipovic & Yerkin Kitapbayev, 2016. "On the American swaption in the linear-rational framework," Papers 1607.02067, arXiv.org, revised Feb 2018.

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