The Effect of the Hurst Parameter on Value at Risk Estimation in Fractional Geometric Brownian motion Price Simulation

This study assessed the impact of the Hurst parameter on the accuracy of Value at Risk (VaR) estimation using fractional Geometric Brownian motion (fGBM) for stock price simulation. The fGBM model, known for its ability to capture long-term memory in financial time series, was employed to simulate stock prices with varying Hurst parameters. The accuracy of VaR estimations obtained from these simulations was then assessed using mean absolute error metric. The research findings revealed that the Hurst parameter significantly influences the accuracy of VaR estimation in fGBM models. The study identified 0.7 as the optimal Hurst parameter value that enhances VaR estimation accuracy, highlighting the importance of incorporating long-term memory effects in risk assessment. The insights have practical implications for investors and financial institutions seeking to enhance risk management practices. The researchers recommended further researches using different levels of Hurst parameters and VaR at different significant levels.