[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2109.09302.html
   My bibliography  Save this paper

On the valuation of multiple reset options: integral equation approach

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2109.09302
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Haoxuan Li & Xiangfeng Yang & Yaodong Ni, 2024. "Pricing of shout option in uncertain financial market," Fuzzy Optimization and Decision Making, Springer, vol. 23(3), pages 449-467, September.
    4. 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.
    5. 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.
    6. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
    7. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
    8. Daniel Doyle & Chris Groendyke, 2018. "Using Neural Networks to Price and Hedge Variable Annuity Guarantees," Risks, MDPI, vol. 7(1), pages 1-19, December.
    9. Tiziano De Angelis & Yerkin Kitapbayev, 2014. "On the optimal exercise boundaries of swing put options," Papers 1407.6860, arXiv.org, revised Jan 2017.
    10. Shuqing Jiang & Zongxia Liang & Weiming Wu, 2010. "Stock loan with Automatic termination clause, cap and margin," Papers 1005.1357, arXiv.org, revised Sep 2010.
    11. Buonaguidi, B., 2023. "An optimal sequential procedure for determining the drift of a Brownian motion among three values," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 320-349.
    12. Dai, Min & Kwok, Yue Kuen, 2005. "Options with combined reset rights on strike and maturity," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1495-1515, September.
    13. Soren Christensen & Albrecht Irle & Stephan Jurgens, 2012. "Optimal multiple stopping with random waiting times," Papers 1205.1966, arXiv.org.
    14. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
    15. Liangchen Li & Michael Ludkovski, 2018. "Stochastic Switching Games," Papers 1807.03893, arXiv.org.
    16. Mrad, Fatma & Hamdi, Haykel & Naoui, Kamel & Abid, Ilyes, 2023. "The GMWB guarantee embedded in Life Insurance Contracts: Fair Value Pricing Problem," Finance Research Letters, Elsevier, vol. 51(C).
    17. Dammann, Felix & Ferrari, Giorgio, 2021. "On an Irreversible Investment Problem with Two-Factor Uncertainty," Center for Mathematical Economics Working Papers 646, Center for Mathematical Economics, Bielefeld University.
    18. Maria B. Chiarolla & Tiziano Angelis & Gabriele Stabile, 2022. "An analytical study of participating policies with minimum rate guarantee and surrender option," Finance and Stochastics, Springer, vol. 26(2), pages 173-216, April.
    19. Belomestny, Denis & Kolodko, Anastasia & Schoenmakers, John G. M., 2009. "Regression methods for stochastic control problems and their convergence analysis," SFB 649 Discussion Papers 2009-026, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    20. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2014. "Optimal initiation of a GLWB in a variable annuity: No Arbitrage approach," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 102-111.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2109.09302. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.