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On the valuation of multiple reset options: integral equation approach

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  • Nazym Azimbayev
  • Yerkin Kitapbayev

Abstract

In this paper, we study a pricing problem of the multiple reset put option, which allows the holder to reset several times a current strike price to obtain an at-the-money European put option. We formulate the pricing problem as a multiple optimal stopping problem, then reduce it to a sequence of single optimal stopping problems and study the associated free-boundary problems. We solve this sequence of problems by induction in the number of remaining reset rights and exploit probabilistic arguments such as local time-space calculus on curves. As a result, we characterize each optimal reset boundary as the unique solution to a nonlinear integral equation and derive the reset premium representations for the option prices. We propose that the multiple reset options can be used as cryptocurrency derivatives and an attractive alternative to standard European options due to the extreme volatility of underlying cryptocurrencies.

Suggested Citation

  • Nazym Azimbayev & Yerkin Kitapbayev, 2021. "On the valuation of multiple reset options: integral equation approach," Papers 2109.09302, arXiv.org.
    • Handle: RePEc:arx:papers:2109.09302
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    References listed on IDEAS

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    1. Min Dai & Yue Kuen Kwok & Lixin Wu, 2004. "Optimal Shouting Policies Of Options With Strike Reset Right," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 383-401, July.
    2. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268, April.
    3. Heath Windcliff & Martin Le Roux & Peter Forsyth & Kenneth Vetzal, 2002. "Understanding the Behavior and Hedging of Segregated Funds Offering the Reset Feature," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(2), pages 107-124.
    4. Windcliff, H. & Forsyth, P. A. & Vetzal, K. R., 2001. "Valuation of segregated funds: shout options with maturity extensions," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 1-21, August.
    5. Tiziano De Angelis & Yerkin Kitapbayev, 2018. "On the Optimal Exercise Boundaries of Swing Put Options," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 252-274, February.
    6. Min Dai & Yue Kuen Kwok & Li Xin Wu, 2003. "Options with Multiple Reset Rights," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(06), pages 637-653.
    7. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
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