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The British Put Option

Author

Listed:
  • Goran Peskir
  • Farman Samee

Abstract

We present a new put option where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Inherent in this is a protection feature which is key to the British put option. Should the option holder believe the true drift of the stock price to be unfavourable (based upon the observed price movements) he can substitute the true drift with the contract drift and minimize his losses. The practical implications of this protection feature are most remarkable as not only can the option holder exercise at or above the strike price to a substantial reimbursement of the original option price (covering the ability to sell in a liquid option market completely endogenously) but also when the stock price movements are favourable he will generally receive higher returns at a lesser price. We derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterized as the unique solution to a nonlinear integral equation. Using these results we perform a financial analysis of the British put option that leads to the conclusions above and shows that with the contract drift properly selected the British put option becomes a very attractive alternative to the classic American put.

Suggested Citation

  • Goran Peskir & Farman Samee, 2011. "The British Put Option," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(6), pages 537-563, April.
  • Handle: RePEc:taf:apmtfi:v:18:y:2011:i:6:p:537-563
    DOI: 10.1080/1350486X.2011.591167
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    Citations

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    Cited by:

    1. Luluwah Al-Fagih, 2015. "The British Knock-Out Put Option," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-32.
    2. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    3. Yerkin Kitapbayev, 2015. "The British Lookback Option with Fixed Strike," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 238-260, July.
    4. 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.
    5. Thomas Kruse & Philipp Strack, 2019. "An Inverse Optimal Stopping Problem for Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 423-439, May.
    6. Shi Qiu & Sovan Mitra, 2018. "Mathematical Properties Of American Chooser Options," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-30, December.
    7. Tim Leung & Peng Liu, 2013. "An Optimal Timing Approach to Option Portfolio Risk Management," Palgrave Macmillan Books, in: Jonathan A. Batten & Peter MacKay & Niklas Wagner (ed.), Advances in Financial Risk Management, chapter 17, pages 391-404, Palgrave Macmillan.
    8. Yue Liu & Nicolas Privault, 2018. "A Recursive Algorithm for Selling at the Ultimate Maximum in Regime-Switching Models," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 369-384, March.

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