Asian Journal of Probability and Statistics

This study explores the impact of additional parameters controlling skewness and kurtosis in the Extended Geometric Brownian Motion (EGBM) model, an extension of the old Brownian motion. Our previous research introduced the EGBM model, demonstrating its potential for improved options pricing. This follow-up study examines the sensitivity of the EGBM model to its skewness and kurtosis parameters, analyzing their impact on options pricing, volatility smile, and risk management. Using numerical simulations and empirical data, we assess the model's performance under various market conditions Our findings show that the EGBM model's parameters significantly improve options pricing accuracy, particularly for out-of-the-money options. Skewness affects the volatility smile's asymmetry, while kurtosis influences its curvature. The model's performance is robust across various market conditions, demonstrating its potential for adaptable risk management. This study advances the understanding of skewness and kurtosis parameters in options pricing models, providing empirical evidence for the EGBM model's effectiveness in capturing complex market dynamics. The EGBM model's versatility and accuracy make it a valuable tool for practitioners and researchers seeking to improve options pricing and risk management strategies.