Estimation of Geometric Brownian Motion Parameters for Oil Price Analysis

Abstract

<p>Geometric Brownian motion (GBM), a stochastic differential equation, can be used to model phenomena that are subject to fluctuation and exhibit long-term trends, such as stock prices and the market value of goods. The model uses two parameters, the rate of drift from previous values and volatility, to describe and predict how the continuous-time stochastic process evolves over time. Accurate estimates of the drift rate and volatility are necessary for these models to be useful within quantitative economic decision-making models. Multiple estimation methods have been proposed in previous research. We show how well these methods perform using a GBM with known parameters using different sample sizes. Using a GBM model, we estimated the parameters for historical oil prices and performed statistical analyses to determine how well the oil prices fit a GBM model.</p>