An Option Valuation Framework Based on Arithmetic Brownian Motion Justification and Implementation Issues

Abstract

We examine arithmetic Brownian motion as an alternative framework for option valuation and related tasks. After re-examining empirical evidence, we compare and contrast option valuation based on one of the simplest forms of geometric Brownian motion with arithmetic Brownian motion. We identify an enhanced way to handle negative stock prices within arithmetic Brownian motion that is consistent with empirical observation. We review numerous strengths and weaknesses of both approaches. The arithmetic Brownian motion framework allows for the aggregation of any number of correlated factors for risk analysis.

Publication
Journal of Financial Research
Robert E. Brooks
Robert E. Brooks
Wallace D. Malone, Jr. Professor of Financial Management

My research interests include financial derivatives, enterprise risk management, performance attribution, options, futures, swaps, and financial philosophy.