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

Author

Listed:
  • 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

Suggested Citation

  • Svetlana Boyarchenko & Sergei Levendorskii, 2006. "General option exercise rules, with applications to embedded options and monopolistic expansion," 2006 Meeting Papers 312, Society for Economic Dynamics.
  • Handle: RePEc:red:sed006:312
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    References listed on IDEAS

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    Cited by:

    1. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    2. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    3. Ferrari, Giorgio & Li, Hanwu & Riedel, Frank, 2020. "A Knightian Irreversible Investment Problem," Center for Mathematical Economics Working Papers 634, Center for Mathematical Economics, Bielefeld University.
    4. 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.
    5. 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.
    6. Sergei Levendorskiĭ, 2022. "Operators and Boundary Problems in Finance, Economics and Insurance: Peculiarities, Efficient Methods and Outstanding Problems," Mathematics, MDPI, vol. 10(7), pages 1-36, March.
    7. Boyarchenko, Svetlana & Levendorskii, Sergei, 2008. "Exit problems in regime-switching models," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 180-206, January.
    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. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    10. Przemys{l}aw Repetowicz & Peter Richmond, 2006. "Option pricing with log-stable L\'{e}vy processes," Papers math/0612691, arXiv.org.
    11. Dehghani Mohammad H., 2014. "Policy Uncertainty and Technology Adoption," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 14(4), pages 1405-1430, October.

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    More about this item

    Keywords

    embedded options; technology adoption; capital expansion;
    All these keywords.

    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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