Arithmetic Brownian motion and real options

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.

► Project value is modelled as arithmetic Brownian motion (ABM). ► Formulas are derived for European calls and puts on ABM. ► A numerical algorithm is derived for complex options and early exercise. ► Cash outflows are modelled as continuous and discrete yields. ► Examples demonstrate the application to real option analysis.