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Optimal stopping made easy

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  • Boyarchenko, Svetlana
  • Levendorskii[caron], Sergei

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.
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Suggested Citation

  • Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    • Handle: RePEc:eee:mateco:v:43:y:2007:i:2:p:201-217
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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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Rainer Baule & Marco Wilkens, 2004. "Lean Trees--A General Approach for Improving Performance of Lattice Models for Option Pricing," Review of Derivatives Research, Springer, vol. 7(1), pages 53-72.
    5. Ben S. Bernanke, 1983. "Irreversibility, Uncertainty, and Cyclical Investment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(1), pages 85-106.
    6. 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.
    7. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
    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 Boyarchenko & Sergei Levendorskii, 2004. "Real options and the universal bad news principle," Finance 0405011, University Library of Munich, Germany.
    10. 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 1-53, June.
    11. S. I. Boyarchenko & S. Z. Levendorskii, 2002. "Pricing of perpetual Bermudan options," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 432-442.
    12. 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.
    13. 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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    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
    • 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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