Paper: arXiv 2405.02919

Authors: Agni Rakshit, Gautam Bandyopadhyay, Tanujit Chakraborty

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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical and asymptotic math framework for analyzing finite difference hedge errors in Black-Scholes. However, it relies primarily on numerical simulations rather than extensive empirical backtesting with real market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze & Reduce Hedge Errors in Black-Scholes Model] --> B[Inputs: Option Sensitivities & Dynamic Market Conditions]
    B --> C[Methodology: Asymptotic Approach via Finite Difference Techniques]
    C --> D[Computational Processes: Theoretical Error Analysis & Numerical Simulations]
    D --> E[Outcomes: Reduced Hedge Errors & Enhanced Model Robustness]
    E --> F[Key Impact: Improved Risk Management & Portfolio Optimization]