Arithmetic Brownian motion and real options

David Richard Alexander, Mengjia Mo and Alan Fraser Stent

European Journal of Operational Research, 2012, vol. 219, issue 1, 114-122

Abstract: We treat real option value when the underlying process is arithmetic Brownian motion (ABM). In contrast to the more common assumption of geometric Brownian motion (GBM) and multiplicative diffusion, with ABM the underlying project value is expressed as an additive process. Its variance remains constant over time rather than rising or falling along with the project’s value, even admitting the possibility of negative values. This is a more compelling paradigm for projects that are managed as a component of overall firm value. After outlining the case for ABM, we derive analytical formulas for European calls and puts on dividend-paying assets as well as a numerical algorithm for American-style and other more complex options based on ABM. We also provide examples of their use.

Keywords: Investment analysis; Real options; Risk-neutral valuation; Arithmetic Brownian motion (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (21)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:219:y:2012:i:1:p:114-122

DOI: 10.1016/j.ejor.2011.12.023

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