Fractional Brownian motion in option pricing and dynamic delta hedging: Experimental simulations

This research examines the impact of fractional Brownian motion (fBm) on option pricing and dynamic delta hedging. Through experimental simulations, we analyze the influence of the Hurst exponent on option price prediction. Our findings highlight the necessity for continuous calibration of the Hurst exponent for a specific market dataset. By estimating option prices using fBm, we evaluate price prediction accuracy and explore fBm’s benefits in option pricing models. We also investigate dynamic delta hedging strategies for call options within the fBm framework, providing an algorithm and code that consider the Hurst exponent. The study’s insights contribute to advancing financial modeling and risk management practices, illuminating the dynamic nature of market phenomena and underscoring calibration’s significance in capturing market dynamics. The findings emphasize the dynamic interplay between the Hurst exponent and option pricing, offering valuable implications for effective risk management strategies. •Continuous Hurst exponent calibration is essential for a market dataset.•In the money, anti-persistence yields lower call option delta; out of the money, persistence results in higher delta.•Estimating the Hurst exponent in real market data improves options price prediction accuracy.•Algorithm and Python code for dynamic delta hedging with fBm-based replicating portfolio.•In loss events, a higher H enhances risk minimization compared to standard Bm in dynamic delta hedging.