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Optimal stopping made easy

Author

Listed:
  • Svetlana Boyarchenko

    (The University of Texas at Austin)

  • Sergey Levendorskiy

    (The University of Texas at Austin)

Abstract

This paper presents a simple discrete time model for valuing real options. A short proof of optimal exercise rules for the standard problems in the real options theory is given in the binomial and trinomial models, and more generally, when the underlying uncertainty is modelled as a random walk on a lattice. The method of the paper is based on the use of the expected present value operators. With straightforward modifications, the method works in discrete time--continuous space, continuous time--continuous space and continuous time--discrete space models.

Suggested Citation

  • Svetlana Boyarchenko & Sergey Levendorskiy, 2004. "Optimal stopping made easy," Finance 0410016, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0410016
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    References listed on IDEAS

    as
    1. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "American options: the EPV pricing model," Annals of Finance, Springer, vol. 1(3), pages 267-292, August.
    2. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    4. Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, vol. 94(3), pages 557-568, June.
    5. Svetlana Boyarchenko & Sergei Levendorski&icaron;, 2007. "Practical Guide To Real Options In Discrete Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(1), pages 311-342, February.
    6. Svetlana Boyarchenko & Sergei Levendorskii, 2004. "Real options and the universal bad news principle," Finance 0405011, EconWPA.
    7. Ben S. Bernanke, 1983. "Irreversibility, Uncertainty, and Cyclical Investment," The Quarterly Journal of Economics, Oxford University Press, vol. 98(1), pages 85-106.
    8. Boyarchenko Svetlana & Levendorskii Sergei Z, 2006. "General Option Exercise Rules, with Applications to Embedded Options and Monopolistic Expansion," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-51, June.
    9. S. I. Boyarchenko & S. Z. Levendorskii, 2002. "Pricing of perpetual Bermudan options," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 432-442.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Citations

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    Cited by:

    1. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "A theory of endogenous time preference, and discounted utility anomalies," Microeconomics 0506005, EconWPA.
    2. 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.
    3. 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.
    4. repec:spr:compst:v:69:y:2009:i:1:p:27-58 is not listed on IDEAS
    5. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "Discount factors ex post and ex ante, and discounted utility anomalies," Microeconomics 0510013, EconWPA, revised 13 Dec 2005.
    6. 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.
    7. Othón M. Moreno, 2014. "Consumption of Durable Goods under Ambiguity," Working Papers 2014-02, Banco de México.
    8. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.
    9. Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    10. GAHUNGU, Joachim & SMEERS, Yves, 2011. "Sufficient and necessary conditions for perpetual multi-assets exchange options," CORE Discussion Papers 2011035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Luis H. R. Alvarez & Teppo A. Rakkolainen, 2006. "A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions," Discussion Papers 9, Aboa Centre for Economics.
    12. Jaap H. Abbring, 2010. "Identification of Dynamic Discrete Choice Models," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 367-394, September.
    13. Relativo, Jona Princess & Sumayang, Mildred & Diasana, Sarah Jean & Murcia, John Vianne, 2016. "Capital Investment Decisions of Micro, Small and Medium Enterprises: The Case of Digos City," MPRA Paper 79574, University Library of Munich, Germany, revised 07 Jun 2017.
    14. Dehghani Mohammad H., 2014. "Policy Uncertainty and Technology Adoption," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 14(4), pages 1-26, October.

    More about this item

    Keywords

    Real options; random walks on lattices; expected present value operators;

    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
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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