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Strategic real options with stochastic volatility in a duopoly model

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  • Huang, Bing
  • Cao, Jiling
  • Chung, Hyuck

Abstract

The investment-timing problem has been considered by many authors under the assumption that the instantaneous volatility of the demand shock is constant. Recently, Ting et al. [9] carried out an asymptotic approach in a monopoly model by letting the volatility parameter follow a stochastic process. In this paper, we consider a strategic game in which two firms compete for a new market under an uncertain demand, and extend the analysis of Ting et al. to duopoly models under different strategic game structures. In particular, we investigate how the additional uncertainty in the volatility affects the investment thresholds and payoffs of players. Several numerical examples and comparison of the results are provided to confirm our analysis.

Suggested Citation

  • Huang, Bing & Cao, Jiling & Chung, Hyuck, 2013. "Strategic real options with stochastic volatility in a duopoly model," MPRA Paper 45731, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:45731
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    References listed on IDEAS

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    1. Ting, Sai Hung Marten & Ewald, Christian-Oliver & Wang, Wen-Kai, 2013. "On the investment–uncertainty relationship in a real option model with stochastic volatility," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 22-32.
    2. Amir, Rabah & Lambson, Val E., 2003. "Entry, exit, and imperfect competition in the long run," Journal of Economic Theory, Elsevier, vol. 110(1), pages 191-203, May.
    3. Yao-Wen Hsu & Bart Lambrecht, 2007. "Preemptive patenting under uncertainty and asymmetric information," Annals of Operations Research, Springer, vol. 151(1), pages 5-28, April.
    4. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    5. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    6. M. R. Grasselli & V. Leclère & M. Ludkovski, 2013. "Priority Option: The Value Of Being A Leader," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-37.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. Graham, Jeffrey, 2011. "Strategic real options under asymmetric information," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 922-934, June.
    9. Marseguerra, Giovanni & Cortelezzi, Flavia & Dominioni, Armando, 2006. "Investment timing decisions in a stochastic duopoly model," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 611-625.
    10. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
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    Cited by:

    1. Kim, Jeong-Hoon & Lee, Min-Ku & Sohn, So Young, 2014. "Investment timing under hybrid stochastic and local volatility," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 58-72.

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    More about this item

    Keywords

    Asymptotic solution; Real option; Stochastic duopoly game; Stochastic volatility.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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