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General Option Exercise Rules, with Applications to Embedded Options and Monopolistic Expansion

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  • Boyarchenko Svetlana

    ()
    (Department of Economics, University of Texas, Austin)

  • Levendorskii Sergei Z

    ()
    (Department of Economics, University of Texas, Austin)

Abstract

This paper provides a general framework for pricing of real options for wide classes of payoff streams that are functions of Levy processes. As applications, we calculate the values of sequences of embedded options, (which we call Russian dolls), and study two models of expansion of a monopoly. In the first model, the monopoly increases capital stock each time the stochastic demand crosses the boundary of the inaction region. Assuming that above a certain level, the stochastic demand factor increases slower than in the standard geometric Levy models, we demonstrate that the investment threshold is lower than in the standard models. Moreover, in the intermediate range between the regimes of the fast and slow growth, the monopoly may find it optimal to simultaneously increase the capital stock and decrease the output price. In a two-factor model of technology adoption, we show that diffusion and jump uncertainty can produce opposite effects.

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Bibliographic Info

Article provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.

Volume (Year): 6 (2006)
Issue (Month): 1 (June)
Pages: 1-51

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Handle: RePEc:bpj:bejtec:v:contributions.6:y:2006:i:1:n:2

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  1. Svetlana Boyarchenko & Sergei Levendorskii, 2004. "American options: the EPV pricing model," Finance 0405024, EconWPA.
  2. Ben S. Bernanke, 1980. "Irreversibility, Uncertainty, and Cyclical Investment," NBER Working Papers 0502, National Bureau of Economic Research, Inc.
  3. Pauli Murto, 2004. "Exit in Duopoly Under Uncertainty," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 111-127, Spring.
  4. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-73, July.
  5. Andrew B. Abel & Janice C. Eberly, 1995. "The Effects of Irreversibility and Uncertainty on Capital Accumulation," NBER Working Papers 5363, National Bureau of Economic Research, Inc.
  6. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
  7. Lander, Diane M. & Pinches, George E., 1998. "Challenges to the Practical Implementation of Modeling and Valuing Real Options," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(3, Part 2), pages 537-567.
  8. Alvarez, Luis H. R. & Stenbacka, Rune, 2001. "Adoption of uncertain multi-stage technology projects: a real options approach," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 71-97, February.
  9. Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, vol. 94(3), pages 557-568, June.
  10. Andrew B. Abel & Avinash Dixit & Janice C. Eberly & Robert S. Pindyck, 1996. "Options, the Value of Capital, and Investment," The Quarterly Journal of Economics, MIT Press, vol. 111(3), pages 753-77, August.
  11. Grenadier, Steven R. & Weiss, Allen M., 1997. "Investment in technological innovations: An option pricing approach," Journal of Financial Economics, Elsevier, vol. 44(3), pages 397-416, June.
  12. Steven R. Grenadier, 2002. "Option Exercise Games: An Application to the Equilibrium Investment Strategies of Firms," Review of Financial Studies, Society for Financial Studies, vol. 15(3), pages 691-721.
  13. Leahy, John V, 1993. "Investment in Competitive Equilibrium: The Optimality of Myopic Behavior," The Quarterly Journal of Economics, MIT Press, vol. 108(4), pages 1105-33, November.
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Cited by:
  1. Svetlana Boyarchenko & Sergey Levendorskiy, 2004. "Optimal stopping made easy," Finance 0410016, EconWPA.
  2. Przemys{\l}aw Repetowicz & Peter Richmond, 2006. "Option pricing with log-stable L\'{e}vy processes," Papers math/0612691, arXiv.org.
  3. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.
  4. Boyarchenko, Svetlana & Levendorskii, Sergei, 2008. "Exit problems in regime-switching models," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 180-206, January.
  5. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
  6. 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.
  7. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Computational Statistics, Springer, vol. 69(1), pages 27-58, March.

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