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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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 43 (2007)
Issue (Month): 2 (February)
Pages: 201-217

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Handle: RePEc:eee:mateco:v:43:y:2007:i:2:p:201-217

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Web page: http://www.elsevier.com/locate/jmateco

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References

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  1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  2. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "American options: the EPV pricing model," Annals of Finance, Springer, Springer, vol. 1(3), pages 267-292, 08.
  3. Bernanke, Ben S, 1983. "Irreversibility, Uncertainty, and Cyclical Investment," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 98(1), pages 85-106, February.
  4. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(1), pages 311-342, 02.
  5. S. I. Boyarchenko & S. Z. Levendorskii, 2002. "Pricing of perpetual Bermudan options," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 2(6), pages 432-442.
  6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 7(3), pages 229-263, September.
  7. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  8. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "General option exercise rules, with applications to embedded options and monopolistic expansion," Finance, EconWPA 0511001, EconWPA.
  9. Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, American Economic Association, vol. 94(3), pages 557-568, June.
  10. Svetlana Boyarchenko & Sergei Levendorskii, 2004. "Real options and the universal bad news principle," Finance, EconWPA 0405011, EconWPA.
  11. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, Springer, vol. 6(2), pages 237-263.
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Cited by:
  1. Jaap H. Abbring, 0000. "Mixed Hitting-Time Models," Tinbergen Institute Discussion Papers, Tinbergen Institute 07-057/3, Tinbergen Institute, revised 11 Aug 2009.
  2. GAHUNGU, Joachim & SMEERS, Yves, 2011. "Sufficient and necessary conditions for perpetual multi-assets exchange options," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2011035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Fernando A. C. C. Fonte & Dalila B. M. M. Fontes, 2007. "Optimal investment timing using Markov jump price processes," FEP Working Papers, Universidade do Porto, Faculdade de Economia do Porto 245, Universidade do Porto, Faculdade de Economia do Porto.
  4. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "A theory of endogenous time preference, and discounted utility anomalies," Microeconomics, EconWPA 0506005, EconWPA.
  5. Luis H. R. Alvarez & Teppo A. Rakkolainen, 2006. "A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions," Discussion Papers, Aboa Centre for Economics 9, Aboa Centre for Economics.
  6. Luis Alvarez & Teppo Rakkolainen, 2010. "Investment timing in presence of downside risk: a certainty equivalent characterization," Annals of Finance, Springer, Springer, vol. 6(3), pages 317-333, July.
  7. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "Discount factors ex post and ex ante, and discounted utility anomalies," Microeconomics, EconWPA 0510013, EconWPA, revised 17 Nov 2005.
  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. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Computational Statistics, Springer, Springer, vol. 69(1), pages 27-58, March.

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