On the applicability of the Geometric Brownian Motion for frontier and developed markets a comparative approach

Abstract

The goal of every investor participating in the stock market is to accurately predict stock prices and gain positive return. This necessity has led to the creation of technical analysis models which attempt to carry out this objective, one of which is the Geometric Brownian Motion (GBM). However, its applicability across different market conditions, ranging from stable developed markets to dynamic frontier markets, has been a subject of ongoing research. This study seeks to investigate the applicability of the Geometric Brownian Motion (GBM) model in predicting stock prices across both developed and frontier markets, using the American S&P 500 Index and the Kenyan NSE 20 Share Index as the main representative cases. The analysis revealed that while the GBM demonstrated strong predictive accuracy in developed markets with stable volatility and normality, its performance in frontier markets was mixed, with periods of market stability yielding better results than volatile, non-normal conditions. These findings emphasize the role of market stability and normality in shaping GBM’s predictive accuracy, while also identifying the challenges posed by non-normal returns and volatility clustering. This study contributes to the discussion on adapting stochastic models for enhanced applicability in frontier markets, providing a foundation for future research and practical applications in financial forecasting.

Key Words: Geometric Brownian Motion (GBM), S&P500, NSE 20, Mean Absolute Percentage Error (MAPE), Developed Markets, Frontier Markets, Volatility, Predictive accuracy.