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Can properly discounted projects follow geometric Brownian motion?

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  • Juho Kanniainen

Abstract

The geometric Brownian motion is routinely used as a dynamic model of underlying project value in real option analysis, perhaps for reasons of analytic tractability. By characterizing a stochastic state variable of future cash flows, this paper considers how transformations between a state variable and cash flows are related to project volatility and drift, and specifies necessary and sufficient conditions for project volatility and drift to be time-varying, a topic that is important for real option analysis because project value and its fluctuation can only seldom be estimated from data. This study also shows how fixed costs can cause project volatility to be mean-reverting. We conclude that the conditions of geometric Brownian motion can only rarely be met, and therefore real option analysis should be based on models of cash flow factors rather than a direct model of project value. Copyright Springer-Verlag 2009

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  • Juho Kanniainen, 2009. "Can properly discounted projects follow geometric Brownian motion?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 435-450, December.
    • Handle: RePEc:spr:mathme:v:70:y:2009:i:3:p:435-450
    DOI: 10.1007/s00186-008-0275-0
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    Cited by:

    1. Ymir Mäkinen & Juho Kanniainen & Moncef Gabbouj & Alexandros Iosifidis, 2019. "Forecasting jump arrivals in stock prices: new attention-based network architecture using limit order book data," Quantitative Finance, Taylor & Francis Journals, vol. 19(12), pages 2033-2050, December.
    2. Ymir Makinen & Juho Kanniainen & Moncef Gabbouj & Alexandros Iosifidis, 2018. "Forecasting of Jump Arrivals in Stock Prices: New Attention-based Network Architecture using Limit Order Book Data," Papers 1810.10845, arXiv.org.
    3. Juho Kanniainen & Robert Pich'e, 2012. "Stock Price Dynamics and Option Valuations under Volatility Feedback Effect," Papers 1209.4718, arXiv.org.
    4. Kanniainen, Juho & Piché, Robert, 2013. "Stock price dynamics and option valuations under volatility feedback effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 722-740.
    5. Reindorp, Matthew J. & Fu, Michael C., 2011. "Capital renewal as a real option," European Journal of Operational Research, Elsevier, vol. 214(1), pages 109-117, October.
    6. Juho Kanniainen & Ye Yue, 2019. "The Arrival of News and Return Jumps in Stock Markets: A Nonparametric Approach," Papers 1901.02691, arXiv.org.

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