IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/5099.html
   My bibliography  Save this paper

Optimal hitting time and perpetual option in a non-Lévy model: application to real options

Author

Listed:
  • Barrieu, Pauline
  • Bellamy, N.

Abstract

We study the perpetual American option characteristics in the case where the underlying dynamics involve a Brownian motion and a point process with a stochastic intensity. No assumption on the distribution of the jump size is made and we work with an arbitrary positive or negative jump. After proving the existence of an optimal stopping time for the problem and characterizing it as the hitting time of an optimal boundary,we provide closed-form formulae for the option value, as well as for the Laplace transform of the optimal stopping time. These results are then applied to the analysis of a real option problem when considering the impact of a fundamental and brutal change in the investment project environment. The consequences of this impact, that can seriously modify, positively or negatively, the project’s future cash flows and therefore the investment decision, are illustrated numerically via the study of some examples.

Suggested Citation

  • Barrieu, Pauline & Bellamy, N., 2007. "Optimal hitting time and perpetual option in a non-Lévy model: application to real options," LSE Research Online Documents on Economics 5099, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:5099
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/5099/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    2. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    3. Marc Chesney & M. Jeanblanc, 2004. "Pricing American currency options in an exponential Levy model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(3), pages 207-225.
    4. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
    5. Pindyck, Robert S, 1993. "A Note on Competitive Investment under Uncertainty," American Economic Review, American Economic Association, vol. 83(1), pages 273-277, March.
    6. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    7. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    8. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    9. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    10. Hans Gerber & Elias Shiu, 1998. "Pricing Perpetual Options for Jump Processes," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(3), pages 101-107.
    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. Marzia De Donno & Zbigniew Palmowski & Joanna Tumilewicz, 2020. "Double continuation regions for American and Swing options with negative discount rate in Lévy models," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 196-227, January.
    2. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    3. Christian Flor & Simon Hansen, 2013. "Technological advances and the decision to invest," Annals of Finance, Springer, vol. 9(3), pages 383-420, August.
    4. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    5. Driver, Ciaran & Temple, Paul & Urga, Giovanni, 2008. "Real options -- delay vs. pre-emption: Do industrial characteristics matter?," International Journal of Industrial Organization, Elsevier, vol. 26(2), pages 532-545, March.
    6. Gapeev Pavel V. & Kühn Christoph, 2005. "Perpetual convertible bonds in jump-diffusion models," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 15-31, January.
    7. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    8. Gapeev, Pavel V., 2008. "The integral option in a model with jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2623-2631, November.
    9. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
    10. Jérôme Detemple & Weidong Tian & Jie Xiong, 2012. "An optimal stopping problem with a reward constraint," Finance and Stochastics, Springer, vol. 16(3), pages 423-448, July.
    11. Gapeev, Pavel V. & Stoev, Yavor I., 2017. "On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 152-162.
    12. repec:hum:wpaper:sfb649dp2006-068 is not listed on IDEAS
    13. repec:dau:papers:123456789/3018 is not listed on IDEAS
    14. Ludovic Mathys, 2019. "Valuing Tradeability in Exponential L\'evy Models," Papers 1912.00469, arXiv.org, revised Feb 2020.
    15. Kogan, Leonid, 2001. "An equilibrium model of irreversible investment," Journal of Financial Economics, Elsevier, vol. 62(2), pages 201-245, November.
    16. Gapeev, Pavel V., 2006. "Integral options in models with jumps," SFB 649 Discussion Papers 2006-068, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    17. N. Bloom, 2016. "Fluctuations in uncertainty," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 4.
    18. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    19. Lund, Diderik, 2006. "Valuation, leverage and the cost of capital in the case of depreciable assets," Working Papers 03-2003, Copenhagen Business School, Department of Economics.
    20. Bar-Ilan, Avner & Strange, William C., 1998. "A model of sequential investment," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 437-463, March.
    21. Tsekrekos, Andrianos E., 2010. "The effect of mean reversion on entry and exit decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 725-742, April.
    22. Nguyen, Minh Hong & Trinh, Vu Quang, 2023. "U.K. economic policy uncertainty and innovation activities: A firm-level analysis," Journal of Economics and Business, Elsevier, vol. 123(C).

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    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:ehl:lserod:5099. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.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.