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Options with Multiple Reset Rights

Author

Listed:
  • Min Dai

    (Department of Financial Mathematics, Laboratory of Mathematics and Applied Mathematics, Peking University, Beijing 100871, China)

  • Yue Kuen Kwok

    (Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

  • Li Xin Wu

    (Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

Abstract

The reset right embedded in a derivative refers to the feature that the holder can alter certain terms in the derivative contract according to some preset rules. In this paper, we consider options that allow the holder to reset the strike price with preset number of times at any moment during the life of the option. The determination of the optimal reset policies adopted by the holder leads to a free boundary value problem. We explore how the critical asset value at which the holder should exercise the reset right optimally depends on the number of reset rights remaining, the relative magnitude of the riskless interest rate and dividend yield, the original strike price set at initiation, etc. In particular, we examine the asymptotic behaviors of the optimal reset policies at infinite time to expiry and the existence of threshold time earlier than which the holder should never shout.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:06:n:s0219024903002146
    DOI: 10.1142/S0219024903002146
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    Citations

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    Cited by:

    1. Chu, Chi Chiu & Kwok, Yue Kuen, 2004. "Reset and withdrawal rights in dynamic fund protection," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 273-295, April.
    2. Nazym Azimbayev & Yerkin Kitapbayev, 2021. "On the valuation of multiple reset options: integral equation approach," Papers 2109.09302, arXiv.org.
    3. Yu-Hong Liu & I-Ming Jiang & Shih-Cheng Lee & Yu-Ting Chen, 2011. "The Valuation Of Reset Options When Underlying Assets Are Autocorrelated," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 5(2), pages 95-114.
    4. Dai, Min & Kwok, Yue Kuen, 2008. "Optimal multiple stopping models of reload options and shout options," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2269-2290, July.
    5. L. Ramprasath, 2011. "Simpler proofs in finance and shout options," Applied Economics Letters, Taylor & Francis Journals, vol. 18(2), pages 173-178.
    6. Guangming Xue & Bin Qin & Guohe Deng, 2018. "Valuation on an Outside-Reset Option with Multiple Resettable Levels and Dates," Complexity, Hindawi, vol. 2018, pages 1-13, April.

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