  The Black-Scholes option pricing model remains a cornerstone in financial
mathematics, yet its application is often challenged by the need for accurate
hedging strategies, especially in dynamic market environments. This paper
presents a rigorous analysis of hedge errors within the Black-Scholes
framework, focusing on the efficacy of finite difference techniques in
calculating option sensitivities. Employing an asymptotic approach, we
investigate the behavior of hedge errors under various market conditions,
emphasizing the implications for risk management and portfolio optimization.
Through theoretical analysis and numerical simulations, we demonstrate the
effectiveness of our proposed method in reducing hedge errors and enhancing the
robustness of option pricing models. Our findings provide valuable insights
into improving the accuracy of hedging strategies and advancing the
understanding of option pricing in financial markets.
