Enhancing Option Pricing Accuracy through Empirical Performance: A GARCH-Based Approach to Refining Volatility Assumptions in the Black-Scholes Model

Abstract

This study presents a comprehensive investigation into enhancing the precision of option pricing by refining the volatility assumption of the Black-Scholes (BS) model through the incorporation of the GARCH model. This study uses a methodical approach that includes rigors comparative analysis, Monte Carlo simulations, and historical data calibration. The findings indicate that, when the GARCH model is combined with the conventional BS model using implied volatility, the RMSE is reduced by about 3.3%. The slight autocorrelation in the sample data's inherent constraints, however, mitigate this improvement. This study emphasizes the significance of model assumption revision for capturing changing market dynamics, making a significant contribution to the conversation on improving option pricing accuracy. This study also acts as a crucial resource for academics and industry professionals navigating the complexity of option pricing and volatility modelling.