IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/122933.html
   My bibliography  Save this paper

On the forward algorithm for stopping problems on continuous-time Markov chains

Author

Listed:
  • Miclo, Laurent
  • Villeneuve, Stéphane

Abstract

This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of this type of American options where the main idea is to build a monotone sequence of almost excessive functions that are associated to hitting times of explicit sets. Under minimal assumptions about the payoff and the Markov chain, we prove that the value function of an American option is characterized by the limit of this monotone sequence.

Suggested Citation

  • Miclo, Laurent & Villeneuve, Stéphane, 2019. "On the forward algorithm for stopping problems on continuous-time Markov chains," TSE Working Papers 19-1009, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:122933
    as

    Download full text from publisher

    File URL: https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2019/wp_tse_1009.pdf
    File Function: Full Text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    2. Sören Christensen, 2014. "A Method For Pricing American Options Using Semi-Infinite Linear Programming," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 156-172, January.
    3. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    4. Isaac Sonin, 1999. "The Elimination algorithm for the problem of optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 111-123, March.
    5. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    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. Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.
    2. Guedes, José & Santos, Pedro, 2016. "Valuing an offshore oil exploration and production project through real options analysis," Energy Economics, Elsevier, vol. 60(C), pages 377-386.
    3. Manuel Guerra & Cláudia Nunes & Carlos Oliveira, 2021. "The optimal stopping problem revisited," Statistical Papers, Springer, vol. 62(1), pages 137-169, February.
    4. Biancardi, Marta & Di Bari, Antonio & Villani, Giovanni, 2021. "R&D investment decision on smart cities: Energy sustainability and opportunity," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    5. Santos, Lúcia & Soares, Isabel & Mendes, Carla & Ferreira, Paula, 2014. "Real Options versus Traditional Methods to assess Renewable Energy Projects," Renewable Energy, Elsevier, vol. 68(C), pages 588-594.
    6. Manley, Bruce & Niquidet, Kurt, 2010. "What is the relevance of option pricing for forest valuation in New Zealand?," Forest Policy and Economics, Elsevier, vol. 12(4), pages 299-307, April.
    7. Dapena, Jose Pablo, 2003. "On the Valuation of Companies with Growth Opportunities," Journal of Applied Economics, Universidad del CEMA, vol. 6(1), pages 1-24, May.
    8. Seiji Harikae & James S. Dyer & Tianyang Wang, 2021. "Valuing Real Options in the Volatile Real World," Production and Operations Management, Production and Operations Management Society, vol. 30(1), pages 171-189, January.
    9. Li, Lingfei & Linetsky, Vadim, 2014. "Optimal stopping in infinite horizon: An eigenfunction expansion approach," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 122-128.
    10. Lee, Shun-Chung & Shih, Li-Hsing, 2010. "Renewable energy policy evaluation using real option model -- The case of Taiwan," Energy Economics, Elsevier, vol. 32(Supplemen), pages 67-78, September.
    11. Madlener, Reinhard & Stoverink, Simon, 2012. "Power plant investments in the Turkish electricity sector: A real options approach taking into account market liberalization," Applied Energy, Elsevier, vol. 97(C), pages 124-134.
    12. Twine, Edgar E. & Kiiza, Barnabas & Bashaasha, Bernard, 2015. "The Flexible Accelerator Model of Investment: An Application to Ugandan Tea- Processing Firms," African Journal of Agricultural and Resource Economics, African Association of Agricultural Economists, vol. 10(1), pages 1-15, March.
    13. Zbigniew Palmowski & Jos'e Luis P'erez & Kazutoshi Yamazaki, 2020. "Double continuation regions for American options under Poisson exercise opportunities," Papers 2004.03330, arXiv.org.
    14. Marcel Boyer & Éric Gravel, 2003. "Real Options at Bell Canada," CIRANO Project Reports 2003rp-01, CIRANO.
    15. Aïd, René & Li, Liangchen & Ludkovski, Michael, 2017. "Capacity expansion games with application to competition in power generation investments," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 1-31.
    16. Naoki Makimoto & Ryuta Takashima, 2023. "Capacity Market and Investments in Power Generations: Risk-Averse Decision-Making of Power Producer," Energies, MDPI, vol. 16(10), pages 1-19, May.
    17. Elias, R.S. & Wahab, M.I.M. & Fang, L., 2016. "The spark spread and clean spark spread option based valuation of a power plant with multiple turbines," Energy Economics, Elsevier, vol. 59(C), pages 314-327.
    18. Kocagil, Ahmet E. & Eduardo, Benjamin E., 1996. "Impacts of new environmental standards on mining industry: The case of Peru," Resource and Energy Economics, Elsevier, vol. 18(3), pages 291-310, October.
    19. Stewart C. Myers & James A. Read, Jr., 2012. "Real Options, Taxes and Financial Leverage," NBER Working Papers 18148, National Bureau of Economic Research, Inc.
    20. Soren Christensen & Albrecht Irle & Julian Peter Lemburg, 2021. "Flexible forward improvement iteration for infinite time horizon Markovian optimal stopping problems," Papers 2111.13443, arXiv.org.

    More about this item

    Keywords

    Markov chains; Optimal Stopping; American option pricing;
    All these keywords.

    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:tse:wpaper:122933. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    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.