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Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk

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  • Christian-Oliver Ewald

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  • Zhaojun Yang

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Abstract

We study the classical real option problem in which an agent faces the decision if and when to invest optimally into a project. The investment is assumed to be irreversible. This problem has been studied by Myers and Majd (Adv Futures Options Res 4:1–21, 1990) for the case of a complete market, in which the risk can be perfectly hedged with an appropriate spanning asset, by McDonald and Siegel (Q J Econ, 101:707–727, 1986), who include the incomplete case but assume that the agent is risk neutral toward idiosyncratic risk, and later by Henderson (Valuing the option to invest in an incomplete market, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=569865 , 2006) who studies the incomplete case with risk aversion toward idiosyncratic risk under the assumption that the project value follows a geometric Brownian motion. We take up Henderson’s utility based approach but assume as suggested by Dixit and Pindyck (Investment under uncertainty, Princeton University Press, Princeton, 1994) as well as others, that the project value follows a geometric mean reverting process. The mean reverting structure of the project value process makes our model richer and economically more meaningful. By using techniques from optimal control theory we derive analytic expressions for the value and the optimal exercise time of the option to invest. Copyright Springer-Verlag 2008

Suggested Citation

  • Christian-Oliver Ewald & Zhaojun Yang, 2008. "Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 97-123, August.
  • Handle: RePEc:spr:mathme:v:68:y:2008:i:1:p:97-123
    DOI: 10.1007/s00186-007-0190-9
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    References listed on IDEAS

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    1. Epstein, D. & Mayor, N. & Schonbucher, P. & Whalley, A. E. & Wilmott, P., 1998. "The valuation of a firm advertising optimally," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(2), pages 149-166.
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    3. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    4. Pindyck, Robert S., 2000. "Irreversibilities and the timing of environmental policy," Resource and Energy Economics, Elsevier, vol. 22(3), pages 233-259, July.
    5. Christian-Oliver Ewald & Aihua Zhang, 2006. "A new technique for calibrating stochastic volatility models: the Malliavin gradient method," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 147-158.
    6. Henderson, Vicky & Hobson, David G., 2002. "Real options with constant relative risk aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 329-355, December.
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    8. Christian-Oliver Ewald, 2005. "Optimal Logarithmic Utility And Optimal Portfolios For An Insider In A Stochastic Volatility Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 301-319.
    9. Alos, Elisa & Ewald, Christian-Oliver, 2007. "Malliavin differentiability of the Heston volatility and applications to option pricing," MPRA Paper 3237, University Library of Munich, Germany.
    10. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
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    Cited by:

    1. Jinqiang Yang & Zhaojun Yang, 2012. "Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 195-217, February.
    2. Ewald, Christian-Oliver & Wang, Wen-Kai, 2010. "Irreversible investment with Cox-Ingersoll-Ross type mean reversion," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 314-318, May.
    3. Zhao, Li & Huang, Wenli & Yang, Chen & Li, Shenghong, 2018. "Hedge fund leverage with stochastic market conditions," International Review of Economics & Finance, Elsevier, vol. 57(C), pages 258-273.
    4. Yang, Zhaojun & Ewald, Christian-Oliver, 2010. "On the non-equilibrium density of geometric mean reversion," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 608-611, April.
    5. Wang, Huamao & Yang, Zhaojun & Zhang, Hai, 2015. "Entrepreneurial finance with equity-for-guarantee swap and idiosyncratic risk," European Journal of Operational Research, Elsevier, vol. 241(3), pages 863-871.

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    More about this item

    Keywords

    Real options; Models of mean-reversion; Optimal control; Incomplete market models; C61; G11; G12; G31; E2;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment

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