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The British Asset-Or-Nothing Put Option

Author

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  • MIN GAO

    (School of Mathematics, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK)

Abstract

Following the economic rationale of Peskir & Samee [The British put option, Applied Mathematical Finance 18 (6), 537–563 (2011); The British call option, Quantitative Finance 13 (1), 95–109 (2013)], we present a new class of asset-or-nothing put option where the holder enjoys the early exercise feature of American asset-or-nothing put option whereupon his payoff is the ‘best prediction’ of the European asset-or-nothing put option payoff under the hypothesis that the true drift equals a contract drift. Based on the observed price movements, the option holder finds that if the true drift of the stock price is unfavorable, then he can substitute it with the contract drift and minimize his losses. The key to the British asset-or-nothing put option is the protection feature 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 favorable he will generally receive high returns. 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. We also analyze the financial meaning of the British asset-or-nothing put option using the results above and show that with the contract drift properly selected, the British asset-or-nothing put option becomes a very attractive alternative to the classic European/American asset-or-nothing put option.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:04:n:s0219024917500303
    DOI: 10.1142/S0219024917500303
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    References listed on IDEAS

    as
    1. Goran Peskir & Farman Samee, 2013. "The British call option," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 95-109, January.
    2. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    3. 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.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Goran Peskir & Farman Samee, 2011. "The British Put Option," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(6), pages 537-563, April.
    6. Yerkin Kitapbayev, 2015. "The British Lookback Option with Fixed Strike," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 238-260, July.
    7. Kristoffer Glover & Goran Peskir & Farman Samee, 2010. "The British Russian Option," Research Paper Series 269, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Kristoffer Glover & Goran Peskir & Farman Samee, 2009. "The British Asian Option," Research Paper Series 249, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. Gukhal, C.R.Chandrasekhar Reddy, 2004. "The compound option approach to American options on jump-diffusions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2055-2074, September.
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    Cited by:

    1. Johannes Hendrik Venter & Pieter Juriaan De Jongh, 2022. "Trading Binary Options Using Expected Profit and Loss Metrics," Risks, MDPI, vol. 10(11), pages 1-21, November.

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