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Irreversible investment with Cox-Ingersoll-Ross type mean reversion

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  • Ewald, Christian-Oliver
  • Wang, Wen-Kai

Abstract

We solve a Dixit and Pindyck type irreversible investment problem in continuous time under the assumption that the project value follows a Cox-Ingersoll-Ross process. This setup works well for modeling foreign direct investment in the framework of real options, when the exchange rate is uncertain and the project value fixed in a foreign currency. We indicate how the solution qualitatively differs from the two classical cases: geometric Brownian motion and geometric mean reversion. Furthermore, we discuss analytical properties of the Cox-Ingersoll-Ross process and demonstrate potential advantages of this process as a model for the project value with regard to the classical ones.

Suggested Citation

  • Ewald, Christian-Oliver & Wang, Wen-Kai, 2010. "Irreversible investment with Cox-Ingersoll-Ross type mean reversion," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 314-318, May.
  • Handle: RePEc:eee:matsoc:v:59:y:2010:i:3:p:314-318
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    References listed on IDEAS

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    1. Carmona, Julio & Leon, Angel, 2007. "Investment option under CIR interest rates," Finance Research Letters, Elsevier, vol. 4(4), pages 242-253, December.
    2. Christian-Oliver Ewald & Zhaojun Yang, 2008. "Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 97-123, August.
    3. Metcalf, Gilbert E. & Hassett, Kevin A., 1995. "Investment under alternative return assumptions Comparing random walks and mean reversion," Journal of Economic Dynamics and Control, Elsevier, vol. 19(8), pages 1471-1488, November.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.),Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    6. Henderson, Vicky & Hobson, David G., 2002. "Real options with constant relative risk aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 329-355, December.
    7. Alos, Elisa & Ewald, Christian-Oliver, 2007. "Malliavin differentiability of the Heston volatility and applications to option pricing," MPRA Paper 3237, University Library of Munich, Germany.
    8. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
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    Citations

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    Cited by:

    1. Ting, Sai Hung Marten & Ewald, Christian-Oliver & Wang, Wen-Kai, 2013. "On the investment–uncertainty relationship in a real option model with stochastic volatility," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 22-32.
    2. 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.
    3. Tim Leung & Zheng Wang, 2019. "Optimal risk-averse timing of an asset sale: trending versus mean-reverting price dynamics," Annals of Finance, Springer, vol. 15(1), pages 1-28, March.
    4. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    5. Tim Leung & Zheng Wang, 2016. "Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics," Papers 1610.08143, arXiv.org.
    6. Bouasker, O. & Letifi, N. & Prigent, J.-L., 2016. "Optimal funding and hiring/firing policies with mean reverting demand," Economic Modelling, Elsevier, vol. 58(C), pages 569-579.
    7. Glover, Kristoffer J. & Hambusch, Gerhard, 2016. "Leveraged investments and agency conflicts when cash flows are mean reverting," Journal of Economic Dynamics and Control, Elsevier, vol. 67(C), pages 1-21.

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