Enhancing Option Pricing Accuracy: Integrating the GARCH Model into the Black-Scholes Model for U.S. Stock Indices

The main objective of this study is to increase the accuracy of option pricing of the Black-Scholes model by integrating GARCH models and analyzing the effectiveness of this method across different industries. This study focuses on the three major U.S. stock indices needed to achieve this goal and derive the results. By applying the GARCH model to options data from these indices, this study shows that the GARCH model significantly enhances the pricing accuracy for SPX and DJIA options while not yielding similar improvements for NDX options. This discrepancy highlights the GARCH model's effectiveness in more stable, less volatile industries like industrials and manufacturing but its reduced utility in the technology sector, where stock price fluctuations are more unpredictable. Finally, This study recommends that investors use the GARCH model in industries such as manufacturing and suggests that future research adopt more accurate and advanced models to enhance option pricing in highly volatile sectors, providing investors with better tools and methodologies.