Mathematically Forecasting Stock Prices with Geometric Brownian Motion

Abstract

Predicting the progression of an unsteady stock market appears to be an impossible task due to the volatile nature of investment portfolios. However, principles such as Geometric Brownian Motion account for random occurrences in a way that can be translated to modeling the stock market. This paper analyzes the Reddy-Clinton equation, a difference equation derived by Krishna Reddy and Vaughan Clinton, with the primary intention of modeling stock price movement over time by utilizing existing metrics. The Reddy-Clinton equation incorporates both a certain and uncertain component to generate a figure which effectively depicts the volatility of the stock market. However, this paper aims to clarify the extent of the unpredictability being accounted for by specifically adjusting ε, the variable representing stochasticity, through an adjusted bell-curve model. Additionally, the model is calculated over multiple iterations, with the resulting values collectively averaged to increase accuracy. The adapted model was applied to the following five stocks of varying sectors: AAPL, OXY, PYPL, MCD, and SPG, and resulted in a MAPE of merely 6.87% over a 6-month period. Overall, the paper proposes an altered rendition of the Reddy-Clinton equation to better account for volatility and output an accurate model of a stock’s performance over a period of time.