Geometric Brownian Motion and Cornish-Fisher Expansion for Stock Price Forecasting and Risk Measurement

Abstract

The mining sector plays a significant role in the national economy but is highly exposed to price volatility driven by environmental, regulatory, and global macroeconomic factors. These fluctuating conditions increase investment uncertainty, particularly for major commodity producers, necessitating a robust framework for price forecasting and risk measurement. This study integrates the Geometric Brownian Motion (GBM) model with Value at Risk (VaR) based on the Cornish-Fisher Expansion (CFE) to provide a more adaptive risk estimation framework. The novelty of this integration lies in combining stochastic price modeling with a distribution adjustment that accounts for skewness and kurtosis, effectively addressing the limitations of traditional models that often assume a normal distribution. In the forecasting phase, the GBM model parameters were estimated, and the performance was evaluated against actual market data. The results demonstrate high predictive accuracy with a Mean Absolute Percentage Error (MAPE) of 3.10%. Furthermore, risk measurements using the VaR-CFE approach provide more realistic and conservative estimates by incorporating the calculated skewness of 0.417 and excess kurtosis of -0.296. At a 99% confidence level for a 5-day holding period, the potential investment risk reached 12.72%, which is significantly more representative of market reality than classical VaR estimates. These findings suggest that the GBM-CFE framework serves as a critical decision-making tool for investors in volatile markets, offering a comprehensive perspective that captures both future price trends and potential extreme financial losses.