Evaluating the Geometric Brownian Motion Model for Gold Price Movements (XAU/USD) across Market Conditions

Abstract

This study evaluates the performance of the Geometric Brownian Motion (GBM) model in predicting prices and estimating the risk of XAU/USD under stable and unstable economic conditions. Daily closing price data are divided into in-sample and out-of-sample periods, where return and volatility parameters are estimated from the in-sample data and applied in Monte Carlo simulations. Prediction accuracy is assessed using the Mean Absolute Percentage Error (MAPE), while risk is measured using Value at Risk (VaR) and Expected Shortfall (ES). The results indicate that MAPE values exceed 20% in both economic conditions, suggesting that the predictive accuracy of the GBM model remains moderate. Although the model performs slightly better during stable periods, the difference is not statistically significant. In contrast, risk estimation results show that VaR and ES range between 58% and 59%, with higher values observed during unstable periods. This reflects an increase in market risk driven by higher volatility. Overall, the findings suggest that while GBM is capable of capturing the general movement of gold prices, it has limitations in accurately predicting price levels and capturing extreme market fluctuations, particularly during periods of economic instability.