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On the investment–uncertainty relationship in a real option model with stochastic volatility


  • Ting, Sai Hung Marten
  • Ewald, Christian-Oliver
  • Wang, Wen-Kai


We consider the classical investment timing problem in a framework where the instantaneous volatility of the project value is itself given by a stochastic process, hence lifting the old question about the investment–uncertainty relationship to a new level. Motivated by the classical cases of Geometric Brownian Motion (GBM) and Geometric Mean Reversion (GMR), we consider processes of similar functional form, but with Heston stochastic volatility replacing the constant volatility in the classical models. We refer to these processes as Heston-GBM and Heston-GMR. For these cases we derive asymptotic solutions for the investment timing problem using the methodology introduced by Fouque et al. (2000). In particular we show that compared to the classical cases with constant volatility, the question of whether additional stochastic volatility increases or decreases the investment threshold depends on the instantaneous correlation between the project value and the stochastic volatility. For the case of Heston-GBM we provide a closed form expression that measures this effect quantitatively; for the case of Heston-GMR we derive the sign of the effect analytically, using a type of maximum principle for ODEs. Various numerical examples are discussed and a comparative analysis is provided.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matsoc:v:66:y:2013:i:1:p:22-32
    DOI: 10.1016/j.mathsocsci.2013.01.005

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    References listed on IDEAS

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    Cited by:

    1. Min-Ku Lee, 2019. "Pricing Perpetual American Lookback Options Under Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1265-1277, March.
    2. 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.
    3. 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.
    4. Huang, Bing & Cao, Jiling & Chung, Hyuck, 2014. "Strategic real options with stochastic volatility in a duopoly model," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 40-51.
    5. Chen, Jilong & Ewald, Christian-Oliver, 2017. "Pricing commodity futures options in the Schwartz multi factor model with stochastic volatility: An asymptotic method," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 144-151.

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