Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function

Abstract

This study introduces a novel analytical method for the Black–Scholes European options model, employing modified log-payoff functions raised to a power. The main motivation for this study stems from the need to develop more efficient and accurate analytical techniques for option pricing, particularly under the assumptions of the Black–Scholes framework. The proposed method utilizes the reduced differential transform method (RDTM), which provides a straightforward, flexible, and precise approach for solving the model. A significant contribution of this work is the ability to swiftly obtain explicit solutions with reduced computational time compared to traditional methods. The research also demonstrates that the sensitivities of the European call and put option prices, commonly known as the “Greeks,” can be effectively captured using this approach. Importantly, this model operates under the assumption that assets follow geometric Brownian motion and do not yield dividends. The findings from this study highlight the potential of RDTM as a powerful tool in the realm of financial mathematics, offering substantial improvements in the computational efficiency and accuracy of option pricing models. • This study presents an advanced technique for the Black–Scholes model using powered modified log-payoff function. • Addressing the need for accuracy, this work improves option pricing in the Black–Scholes model. • The method precisely captures European call and put option sensitivities, known as the “Greeks”. • The model assumes asset prices follow geometric Brownian motion without dividend yields. • This study identifies RDTM as a revolutionary tool, enhancing efficiency and accuracy in option pricing.