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Practical guide to real options in discrete time

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  • Svetlana Boyarchenko
  • Sergei Levendorskii

Abstract

Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general, computationally simple approach to real options in discrete time. Explicit formulas are derived even for embedded options. Discrete time processes reflect the scarcity of observations in the data, and may account for fat tails and skewness of probability distributions of commodity prices. The method of the paper is based on the use of the expected present value operators.

Suggested Citation

  • Svetlana Boyarchenko & Sergei Levendorskii, 2004. "Practical guide to real options in discrete time," Papers cond-mat/0404106, arXiv.org.
  • Handle: RePEc:arx:papers:cond-mat/0404106
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    References listed on IDEAS

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    1. Angus Deaton & Guy Laroque, 1992. "On the Behaviour of Commodity Prices," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 1-23.
    2. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955, December.
    3. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    4. Thomas F. Cooley & Vincenzo Quadrini, 2001. "Financial Markets and Firm Dynamics," American Economic Review, American Economic Association, vol. 91(5), pages 1286-1310, December.
    5. Abel, Andrew B. & Eberly, Janice C., 1999. "The effects of irreversibility and uncertainty on capital accumulation," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 339-377, December.
    6. S. I. Boyarchenko & S. Z. Levendorskii, 2002. "Pricing of perpetual Bermudan options," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 432-442.
    7. Steven J. Davis & John C. Haltiwanger & Scott Schuh, 1998. "Job Creation and Destruction," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262540932, January.
    8. Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, vol. 94(3), pages 557-568, June.
    9. Svetlana I. Boyarchenko & Sergei Z. Levendorskiĭ, 2002. "Perpetual American options," World Scientific Book Chapters,in: Non-Gaussian Merton-Black-Scholes Theory, chapter 5, pages 121-149 World Scientific Publishing Co. Pte. Ltd..
    10. Seung-Ryong Yang & B. Wade Brorsen, 1992. "Nonlinear Dynamics of Daily Cash Prices," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 74(3), pages 706-715.
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    Citations

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    Cited by:

    1. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "American options: the EPV pricing model," Annals of Finance, Springer, vol. 1(3), pages 267-292, August.
    2. Detert, Neal & Kotani, Koji, 2013. "Real options approach to renewable energy investments in Mongolia," Energy Policy, Elsevier, vol. 56(C), pages 136-150.
    3. Jukka Lempa, 2008. "On infinite horizon optimal stopping of general random walk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 257-268, April.
    4. Luis Alvarez & Teppo Rakkolainen, 2010. "Investment timing in presence of downside risk: a certainty equivalent characterization," Annals of Finance, Springer, vol. 6(3), pages 317-333, July.
    5. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 27-58, March.
    6. repec:spr:compst:v:69:y:2009:i:1:p:27-58 is not listed on IDEAS
    7. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "Discount factors ex post and ex ante, and discounted utility anomalies," Microeconomics 0510013, EconWPA, revised 13 Dec 2005.
    8. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    9. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "A theory of endogenous time preference, and discounted utility anomalies," Microeconomics 0506005, EconWPA.
    10. repec:spr:compst:v:67:y:2008:i:2:p:257-268 is not listed on IDEAS
    11. Fernando A. C. C. Fonte & Dalila B. M. M. Fontes, 2007. "Optimal investment timing using Markov jump price processes," FEP Working Papers 245, Universidade do Porto, Faculdade de Economia do Porto.
    12. Boyarchenko, Svetlana & Levendorskii, Sergei, 2008. "Exit problems in regime-switching models," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 180-206, January.
    13. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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