Hedge Error Analysis In Black Scholes Option Pricing Model: An Asymptotic Approach Towards Finite Difference

TL;DR

This paper analyzes hedge errors in the Black-Scholes model using an asymptotic approach, demonstrating how finite difference methods can improve hedging accuracy and robustness in dynamic markets.

Contribution

It introduces an asymptotic analysis of hedge errors with finite difference techniques, offering new insights into error reduction and model robustness.

Findings

Finite difference methods can significantly reduce hedge errors.

Asymptotic analysis provides deeper understanding of error behavior.

Numerical simulations confirm improved hedging strategies.

Abstract

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.