Can Properly Discounted Projects Follow Geometric Brownian Motion?

Posted: 3 Nov 2012

Date Written: December 5, 2008

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.

Keywords: Real options, Stochastic processes, Geometric Brownian motion, Stochastic volatility, Present value model

Suggested Citation

Kanniainen, Juho, Can Properly Discounted Projects Follow Geometric Brownian Motion? (December 5, 2008). Mathematical Methods of Operations Research, Vol. 70, No. 3,pp 435-450, 2009, Available at SSRN: https://ssrn.com/abstract=2169219

Juho Kanniainen (Contact Author)

Tampere University ( email )

P.O. 541, Korkeakoulunkatu 8 (Festia building)
Tampere, FI-33101
Finland

HOME PAGE: http://https://sites.google.com/site/juhokanniainen/

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