IDEAS home Printed from https://ideas.repec.org/a/bla/jbfnac/v31y2004i9-10p1449-1481.html
   My bibliography  Save this article

A Modified ‘Square Root’ Process for Determining the Value of the Option to (Dis)invest

Author

Listed:
  • Paul Klumpes
  • Mark Tippett

Abstract

We determine optimal investment criteria for a capital project whose cash flows evolve in terms of a ‘modified square root’ process. The modified square root process has properties similar to the Cox, Ingersoll and Ross (1985)‘square root’ process but in addition, encompasses the possibility of negative cash flows. Although closed form solutions for the valuation equations implied by the modified square root process are the exception rather than the rule we are able to show that analytic solutions, in the form of infinite power series expansions, will always exist. Furthermore, we also show that when a prescribed set of regularity conditions is satisfied, these power series expansions converge to closed form valuation functions. The optimality criteria for capital investment decisions are then simplified considerably.

Suggested Citation

  • Paul Klumpes & Mark Tippett, 2004. "A Modified ‘Square Root’ Process for Determining the Value of the Option to (Dis)invest," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(9‐10), pages 1449-1481, November.
    • Handle: RePEc:bla:jbfnac:v:31:y:2004:i:9-10:p:1449-1481
    DOI: 10.1111/j.0306-686X.2004.00580.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.0306-686X.2004.00580.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.0306-686X.2004.00580.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Huw Rhys & Mark Tippet, 2001. "A Binomial Basis for the Cox, Ingersoll and Ross Model of the Term Structure of Interest Rates," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 28(3-4), pages 379-405.
    2. 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.
    3. Huw Rhys & Mark Tippet, 2001. "A Binomial Basis for the Cox, Ingersoll and Ross Model of the Term Structure of Interest Rates," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 28(3‐4), pages 379-405, April.
    4. Black, Fischer, 1995. "Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-1376, December.
    5. Miles, David, 1993. "Testing for Short Termisn in the UK Stock Market," Economic Journal, Royal Economic Society, vol. 103(421), pages 1379-1396, November.
    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. Clark, Ephraim & Lakshmi, Geeta, 2007. "Assymetric information and the pricing of sovereign eurobonds: India 1990-1992," Global Finance Journal, Elsevier, vol. 18(1), pages 124-142.
    2. Qian Guo & Huw Rhys & Xiaojing Song & Mark Tippett, 2016. "The Friedman rule and inflation targeting," The European Journal of Finance, Taylor & Francis Journals, vol. 22(14), pages 1414-1434, November.
    3. Oscar Gutiérrez & Francisco Ruiz-Aliseda, 2011. "Real options with unknown-date events," Annals of Finance, Springer, vol. 7(2), pages 171-198, May.
    4. Arve, Malin & Zwart, Gijsbert, 2023. "Optimal procurement and investment in new technologies under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 147(C).
    5. Tan Wang & Tony S. Wirjanto, 2016. "Risk Aversion, Uncertainty, Unemployment Insurance Benefit and Duration of "Wait" Unemployment," Annals of Economics and Finance, Society for AEF, vol. 17(1), pages 1-34, May.
    6. Stephen Nickell & John Van Reenen, 2001. "Technological Innovation and Performance in the United Kingdom," CEP Discussion Papers dp0488, Centre for Economic Performance, LSE.
    7. Song, Dandan & Wang, Huamao & Yang, Zhaojun, 2014. "Learning, pricing, timing and hedging of the option to invest for perpetual cash flows with idiosyncratic risk," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 1-11.
    8. Gabriel J Power & Charli D. Tandja M. & Josée Bastien & Philippe Grégoire, 2015. "Measuring infrastructure investment option value," Journal of Risk Finance, Emerald Group Publishing, vol. 16(1), pages 49-72, January.
    9. Lotfaliei, Babak, 2018. "Zero leverage and the value in waiting to have debt," Journal of Banking & Finance, Elsevier, vol. 97(C), pages 335-349.
    10. Anni Huang & Narayan Kundan Kishor, 2019. "The rise of dollar credit in emerging market economies and US monetary policy," The World Economy, Wiley Blackwell, vol. 42(2), pages 530-551, February.
    11. Alan Carruth & Andy Dickerson & Andrew Henley, 2000. "What do We Know About Investment Under Uncertainty?," Journal of Economic Surveys, Wiley Blackwell, vol. 14(2), pages 119-154, April.
    12. Wong, Kit Pong, 2008. "Does market demand volatility facilitate collusion?," Economic Modelling, Elsevier, vol. 25(4), pages 696-703, July.
    13. John P. Small & Henry Ergas, 1999. "The Rental Cost of Sunk and Regulated Capital," Econometrics Working Papers 9908, Department of Economics, University of Victoria.
    14. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    15. 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.
    16. Feil, Jan-Henning & Musshoff, Oliver, 2013. "Investment, disinvestment and policy impact analysis in the dairy sector: a real options approach," Structural Change in Agriculture/Strukturwandel im Agrarsektor (SiAg) Working Papers 159229, Humboldt University Berlin, Department of Agricultural Economics.
    17. Arman Avadikyan & Patrick Llerena, 2009. "Socio-technical transition processes: A real option based reasoning," Working Papers of BETA 2009-21, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    18. Tauer, Loren W., 2006. "When to Get In and Out of Dairy Farming: A Real Option Analysis," Agricultural and Resource Economics Review, Cambridge University Press, vol. 35(2), pages 339-347, October.
    19. Adam Traczyk, 2013. "Financial integration and the term structure of interest rates," Empirical Economics, Springer, vol. 45(3), pages 1267-1305, December.
    20. Yishay D. Maoz, 2011. "Tax, Stimuli Of Investment And Firm Value," Metroeconomica, Wiley Blackwell, vol. 62(1), pages 171-174, February.

    More about this item

    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:bla:jbfnac:v:31:y:2004:i:9-10:p:1449-1481. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0306-686X .

    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.