IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v13y2025i6p112-d1678169.html
   My bibliography  Save this article

Evaluation of Perpetual American Put Options with General Payoff

Author

Listed:
  • Luca Anzilli

    (Department of Economic Sciences, University of Salento, 73100 Lecce, Italy)

  • Lucianna Cananà

    (Ionian Department of Law, Economics and Environment, University of Bari “Aldo Moro”, 74121 Taranto, Italy)

Abstract

In this paper, we study perpetual American put options with a generalized standard put payoff and establish sufficient conditions for the existence and uniqueness of the solution to the associated pricing problem. As a key tool, we express the Black–Scholes operator in terms of elasticity. This formulation enables us to demonstrate that the considered pricing problem admits a unique solution when the payoff function exhibits strictly decreasing elasticity with respect to the underlying asset. Furthermore, this approach allows us to derive closed-form solutions for option pricing.

Suggested Citation

  • Luca Anzilli & Lucianna Cananà, 2025. "Evaluation of Perpetual American Put Options with General Payoff," Risks, MDPI, vol. 13(6), pages 1-20, June.
    • Handle: RePEc:gam:jrisks:v:13:y:2025:i:6:p:112-:d:1678169
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/13/6/112/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/13/6/112/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2021. "Valuation of piecewise linear barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    2. Lee, Jung-Kyung, 2020. "A simple numerical method for pricing American power put options," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Donald Aingworth & Sanjiv Das & Rajeev Motwani, 2006. "A simple approach for pricing equity options with Markov switching state variables," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 95-105.
    4. Gordon Sick & Andrea Gamba, 2010. "Some Important Issues Involving Real Options: An Overview," Multinational Finance Journal, Multinational Finance Journal, vol. 14(1-2), pages 73-123, March-Jun.
    5. Johnson, Paul & Szabó, Dávid Zoltán & Duck, Peter, 2024. "Optimal trading with regime switching: Numerical and analytic techniques applied to valuing storage in an electricity balancing market," European Journal of Operational Research, Elsevier, vol. 319(2), pages 611-624.
    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. Massimo Guidolin, 2013. "Markov switching models in asset pricing research," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 1, pages 3-44, Edward Elgar Publishing.
    2. Michael C. Fu & Bingqing Li & Rongwen Wu & Tianqi Zhang, 2020. "Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model," Papers 2006.15054, arXiv.org.
    3. Lee, Hangsuck & Ha, Hongjun & Lee, Gaeun & Lee, Minha, 2024. "Valuing American options using multi-step rebate options," The North American Journal of Economics and Finance, Elsevier, vol. 74(C).
    4. Marcel Philipp Müller & Sebastian Stöckl & Steffen Zimmermann & Bernd Heinrich, 2016. "Decision Support for IT Investment Projects," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 58(6), pages 381-396, December.
    5. Bhat, Harish S. & Kumar, Nitesh, 2012. "Option pricing under a normal mixture distribution derived from the Markov tree model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 762-774.
    6. Qinjing Qiu & Reiichiro Kawai, 2023. "Iterative Weak Approximation and Hard Bounds for Switching Diffusion," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1003-1036, June.
    7. Schachter, J.A. & Mancarella, P., 2016. "A critical review of Real Options thinking for valuing investment flexibility in Smart Grids and low carbon energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 261-271.
    8. Dahlgren, Eric & Leung, Tim, 2015. "An optimal multiple stopping approach to infrastructure investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 251-267.
    9. Xinyue Wei & Cuilian You & Yujie Zhang, 2023. "European Option Pricing Under Fuzzy CEV Model," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 415-432, February.
    10. Jung Ho Park & Kwangsoo Shin, 2018. "R&D Project Valuation Considering Changes of Economic Environment: A Case of a Pharmaceutical R&D Project," Sustainability, MDPI, vol. 10(4), pages 1-15, March.
    11. Kryukov, V. A. & Sevastyanova, A. Ye. & Tokarev, A. N. & Shmat , V. V., 2016. "A rationale for some directions of the development of resource territories: the complex ''meso-level'' problem," R-Economy, Ural Federal University, Graduate School of Economics and Management, vol. 2(1), pages 38-50.
    12. Emilio Russo, 2020. "A Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model," Risks, MDPI, vol. 8(1), pages 1-22, January.
    13. Vitaliy Golomoziy & Kamil Kladivko & Yuliya Mishura, 2025. "Discrete-time weak approximation of a Black-Scholes model with drift and volatility Markov switching," Papers 2501.06895, arXiv.org.
    14. Oscar V. De la Torre-Torres & Francisco Venegas-Martínez & Mᵃ Isabel Martínez-Torre-Enciso, 2021. "Enhancing Portfolio Performance and VIX Futures Trading Timing with Markov-Switching GARCH Models," Mathematics, MDPI, vol. 9(2), pages 1-22, January.
    15. Zhang, Xiaoyuan & Zhang, Tianqi, 2023. "On pricing double-barrier options with Markov regime switching," Finance Research Letters, Elsevier, vol. 51(C).
    16. Chinonso Nwankwo & Weizhong Dai, 2020. "Explicit RKF-Compact Scheme for Pricing Regime Switching American Options with Varying Time Step," Papers 2012.09820, arXiv.org, revised Feb 2022.
    17. Chandra, Atul & Hartley, Peter R., 2024. "Sequential investment decisions for mining projects using compound multiple volatility real options approach," Resources Policy, Elsevier, vol. 97(C).
    18. Chen Tong & Peter Reinhard Hansen & Zhuo Huang, 2022. "Option pricing with state‐dependent pricing kernel," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(8), pages 1409-1433, August.
    19. Hangsuck Lee & Hongjun Ha & Minha Lee, 2022. "Piecewise linear boundary crossing probabilities, barrier options, and variable annuities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(12), pages 2248-2272, December.
    20. Junkee Jeon & Geonwoo Kim, 2022. "Analytic Valuation Formula for American Strangle Option in the Mean-Reversion Environment," Mathematics, MDPI, vol. 10(15), pages 1-19, July.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:gam:jrisks:v:13:y:2025:i:6:p:112-:d:1678169. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.