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Real-Option Valuation in Multiple Dimensions Using Poisson Optional Stopping Times

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  • Lange, Rutger-Jan
  • Ralph, Daniel
  • Støre, Kristian

Abstract

We provide a new framework for valuing multidimensional real options where opportunities to exercise the option are generated by an exogenous Poisson process, which can be viewed as a liquidity constraint on decision times. This approach, which we call the Poisson optional stopping times (POST) method, finds the value function as a monotone sequence of lower bounds. In a case study, we demonstrate that the frequently used quasi-analytic method yields a suboptimal policy and an inaccurate value function. The proposed method is demonstrably correct, straightforward to implement, reliable in computation, and broadly applicable in analyzing multidimensional option-valuation problems.

Suggested Citation

  • Lange, Rutger-Jan & Ralph, Daniel & Støre, Kristian, 2020. "Real-Option Valuation in Multiple Dimensions Using Poisson Optional Stopping Times," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(2), pages 653-677, March.
    • Handle: RePEc:cup:jfinqa:v:55:y:2020:i:2:p:653-677_9
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    Cited by:

    1. 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.
    2. Rutger-Jan Lange & Coen N. Teulings, 2021. "The option value of vacant land: Don't build when demand for housing is booming," Tinbergen Institute Discussion Papers 21-022/IV, Tinbergen Institute.
    3. Nunes, Cláudia & Oliveira, Carlos & Pimentel, Rita, 2021. "Quasi-analytical solution of an investment problem with decreasing investment cost due to technological innovations," Journal of Economic Dynamics and Control, Elsevier, vol. 130(C).
    4. Lange, Rutger-Jan & Teulings, Coen N., 2024. "Irreversible investment under predictable growth: Why land stays vacant when housing demand is booming," Journal of Economic Theory, Elsevier, vol. 215(C).
    5. Tine Compernolle & Kuno J. M. Huisman & Peter M. Kort & Maria Lavrutich & Cláudia Nunes & Jacco J. J. Thijssen, 2021. "Investment Decisions with Two-Factor Uncertainty," JRFM, MDPI, vol. 14(11), pages 1-17, November.
    6. Alvarez E., Luis H.R. & Lempa, Jukka & Saarinen, Harto & Sillanpää, Wiljami, 2024. "Solutions for Poissonian stopping problems of linear diffusions via extremal processes," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    7. Takuji Arai & Masahiko Takenaka, 2022. "Constrained optimal stopping under a regime-switching model," Papers 2204.07914, arXiv.org.
    8. Zhang, Xinhua & Hueng, C. James & Lemke, Robert J., 2023. "Using a price floor on carbon allowances to achieve emission reductions under uncertainty," Economic Analysis and Policy, Elsevier, vol. 80(C), pages 1096-1110.
    9. Hobson, David, 2021. "The shape of the value function under Poisson optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 229-246.
    10. Felix Dammann & Giorgio Ferrari, 2021. "On an Irreversible Investment Problem with Two-Factor Uncertainty," Papers 2103.08258, arXiv.org, revised Jul 2021.
    11. Balter, Anne G. & Huisman, Kuno J.M. & Kort, Peter M., 2022. "New insights in capacity investment under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).

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