IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/33130.html
   My bibliography  Save this paper

Some results on optimally exercising American put options for time-inhomogeneous processes

Author

Listed:
  • D'Auria, Bernardo
  • García Portugués, Eduardo
  • Guada, Abel

Abstract

We solve the finite-horizon, discounted, Mayer optimal stopping problem, with the gain function coming for exercising an American put option, and the underlying process modeled by adiffusion with constant volatility and a time-dependent drift satisfying certain regularity conditions. Both the corresponding value function and optimal stopping boundary are proved to be Lipschitz continuous away from the terminal time. The optimal stopping boundary is characterizedas the unique solution, up to mild regularity conditions, of the free-boundary equation. When the underlying process has Gaussian marginal distributions, more tractable expressions for the pricing formula and free-boundary equation are provided. Finally, we check that an Ornstein&-Uhlenbeck process with time-dependent parameters fulfills the required conditions assumed throughout the paper.

Suggested Citation

  • D'Auria, Bernardo & García Portugués, Eduardo & Guada, Abel, 2021. "Some results on optimally exercising American put options for time-inhomogeneous processes," DES - Working Papers. Statistics and Econometrics. WS 33130, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:33130
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/33130/ws202105.pdf?sequence=1
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Albano, G. & Giorno, V., 2020. "Inferring time non-homogeneous Ornstein Uhlenbeck type stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    2. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
    3. Tiziano De Angelis & Erik Ekstrom, 2016. "The dividend problem with a finite horizon," Papers 1609.01655, arXiv.org, revised Nov 2017.
    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. Giorgio Ferrari & Shihao Zhu, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Papers 2311.12169, arXiv.org.
    2. Tiziano Angelis & Gabriele Stabile, 2019. "On the free boundary of an annuity purchase," Finance and Stochastics, Springer, vol. 23(1), pages 97-137, January.
    3. Tiziano De Angelis & Alessandro Milazzo, 2019. "Optimal stopping for the exponential of a Brownian bridge," Papers 1904.00075, arXiv.org, revised Nov 2019.
    4. Ferrari, Giorgio & Zhu, Shihao, 2022. "Consumption Descision, Portfolio Choice and Healthcare Irreversible Investment," Center for Mathematical Economics Working Papers 671, Center for Mathematical Economics, Bielefeld University.
    5. Giorgio Ferrari & Shihao Zhu, 2022. "On a Merton Problem with Irreversible Healthcare Investment," Papers 2212.05317, arXiv.org, revised Dec 2023.
    6. Ferrari, Giorgio & Zhu, Shihao, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Center for Mathematical Economics Working Papers 683, Center for Mathematical Economics, Bielefeld University.
    7. 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.
    8. 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.
    9. 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.
    10. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2021. "The American put with finite-time maturity and stochastic interest rate," Papers 2104.08502, arXiv.org, revised Feb 2024.
    11. Weiping Li & Su Chen, 2018. "The Early Exercise Premium In American Options By Using Nonparametric Regressions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-29, November.
    12. Felix Dammann & Giorgio Ferrari, 2023. "Optimal execution with multiplicative price impact and incomplete information on the return," Finance and Stochastics, Springer, vol. 27(3), pages 713-768, July.
    13. Tiziano De Angelis, 2018. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Papers 1805.12035, arXiv.org, revised Mar 2019.
    14. Johnson, P. & Pedersen, J.L. & Peskir, G. & Zucca, C., 2022. "Detecting the presence of a random drift in Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1068-1090.
    15. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes," Papers 2211.04095, arXiv.org, revised Dec 2023.
    16. Dammann, Felix & Ferrari, Giorgio, 2022. "Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return," Center for Mathematical Economics Working Papers 663, Center for Mathematical Economics, Bielefeld University.
    17. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Dec 2023.
    18. Pavel V. Gapeev, 2006. "Discounted Optimal Stopping for Maxima in Diffusion Models with Finite Horizon," SFB 649 Discussion Papers SFB649DP2006-057, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    19. Basei, Matteo & Ferrari, Giorgio & Rodosthenous, Neofytos, 2023. "Uncertainty over Uncertainty in Environmental Policy Adoption: Bayesian Learning of Unpredictable Socioeconomic Costs," Center for Mathematical Economics Working Papers 677, Center for Mathematical Economics, Bielefeld University.
    20. Duistermaat, J.J. & Kyprianou, A.E. & van Schaik, K., 2005. "Finite expiry Russian options," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 609-638, April.

    More about this item

    Keywords

    American Put Option;

    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:cte:wsrepe:33130. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.