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General option exercise rules, with applications to embedded options and monopolistic expansion

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  • Svetlana Boyarchenko
  • Sergei Levendorskii

    ()
    (The University of Texas at Austin)

Abstract

This paper provides a general framework for pricing of real options in continuous time for wide classes of payoff streams that are functions of Levy processes. As applications, we calculate the option values of multi-stage investment/disinvestment problems (sequences of embedded options, which we call Russian dolls), and study two models of expansion of a monopoly. In the first model, each time when the stochastic demand reaches the boundary of the inaction region or crosses it, the monopoly increases capital stock but uses the same production technology. We assume that above a certain level, the stochastic demand factor increases slower than in the standard geometric Levy models, and demonstrate that then the investment threshold is lower than in the standard models. Moreover, in the intermediate range between the regimes of the fast and slower growth, the monopoly may find it optimal to simultaneously increase the capital stock and decrease the output price. The second model is driven by two factors: one factor follows a process with upward jumps and describes the dynamics of the frontier technology, the other - demand uncertainty. The impact of these factors on new technology adoption is analyzed. It is shown that depending on the situation and type of uncertainty, the diffusion uncertainty and jump uncertainty can produce opposite effects

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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2006 Meeting Papers with number 312.

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Date of creation: 03 Dec 2006
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Handle: RePEc:red:sed006:312

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Keywords: embedded options; technology adoption; capital expansion;

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References

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  1. Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, vol. 94(3), pages 557-568, June.
  2. Svetlana Boyarchenko & Sergei Levendorskii, 2004. "American options: the EPV pricing model," Finance 0405024, EconWPA.
  3. Andrew B. Abel & Avinash K. Dixit & Janice C. Eberly & Robert S. Pindyck, 1996. "Options, the Value of Capital, and Investment," NBER Working Papers 5227, National Bureau of Economic Research, Inc.
  4. 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.
  5. Ben S. Bernanke, 1980. "Irreversibility, Uncertainty, and Cyclical Investment," NBER Working Papers 0502, National Bureau of Economic Research, Inc.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  12. 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.
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Cited by:
  1. 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.
  2. Xia Su & Frank Riedel, 2006. "On Irreversible Investment," Bonn Econ Discussion Papers bgse13_2006, University of Bonn, Germany.
  3. Przemys{\l}aw Repetowicz & Peter Richmond, 2006. "Option pricing with log-stable L\'{e}vy processes," Papers math/0612691, arXiv.org.
  4. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.

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