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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.

Suggested Citation

  • 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.
  • Handle: RePEc:bpj:bejtec:v:contributions.6:y:2006:i:1:n:2
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    References listed on IDEAS

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    1. Svetlana Boyarchenko & Sergei Levendorskii, 2005. "American options: the EPV pricing model," Annals of Finance, Springer, vol. 1(3), pages 267-292, August.
    2. Andrew B. Abel & Avinash K. Dixit & Janice B. Eberly & Robert S. Pindyck, "undated". "Options, the Value of Capital, and Investment," Rodney L. White Center for Financial Research Working Papers 15-95, Wharton School Rodney L. White Center for Financial Research.
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    Citations

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    Cited by:

    1. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    2. 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.
    3. repec:spr:compst:v:69:y:2009:i:1:p:27-58 is not listed on IDEAS
    4. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    5. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    6. Przemys{l}aw Repetowicz & Peter Richmond, 2006. "Option pricing with log-stable L\'{e}vy processes," Papers math/0612691, arXiv.org.
    7. 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.
    8. Boyarchenko, Svetlana & Levendorskii, Sergei, 2008. "Exit problems in regime-switching models," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 180-206, January.
    9. Boyarchenko, Svetlana & Levendorskii, Sergei, 2010. "Optimal stopping in Levy models, for non-monotone discontinuous payoffs," MPRA Paper 27999, University Library of Munich, Germany.

    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
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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