Another Look at Option Valuation Based on Arithmetic Brownian Motion

Abstract

We take another look at arithmetic Brownian motion as a framework for developing financial derivatives valuation and risk management tools. We compare and contrast option valuation based on geometric Brownian motion and arithmetic Brownian motion. An alternative way to handle negative stock prices within the arithmetic Brownian motion approach is identified that is more consistent with empirical observation than the traditional approach of assuming no possibility of zero prices within the geometric Brownian motion. After comparing a wide array of sensitivities with both models, we discuss numerous strengths and weakness of both approaches. Option valuation based on arithmetic Brownian motion appears to be a credible additional tool for financial quantitative analysis.