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.

本研究探讨了分数布朗运动 (fBm) 对期权定价和动态 Delta 对冲的影响。通过实验模拟，我们分析了赫斯特指数对期权价格预测的影响。我们的研究结果强调了针对特定市场数据集持续校准赫斯特指数的必要性。通过使用 fBm 估计期权价格，我们评估了价格预测的准确性并探索了 fBm 在期权定价模型中的优势。我们还研究了 fBm 框架内看涨期权的动态 Delta 对冲策略，提供了考虑 Hurst 指数的算法和代码。该研究的见解有助于推进金融建模和风险管理实践，阐明市场现象的动态本质，并强调校准在捕捉市场动态方面的重要性。研究结果强调了赫斯特指数和期权定价之间的动态相互作用，为有效的风险管理策略提供了宝贵的启示。