Reduced Differential Transform Method for Solving Modified- Log Payoff Function of European Style Call Option Model

Solving Method for European Style Model

Abstract

This study introduces the Reduced Differential Transform Method (RDTM) as a novel and efficient approach for solving the European Style Call Option Model (ESCOM) using the Modified Log- Payoff Function (MLPF). It begins with a comprehensive overview of RDTM, including its theoretical framework, inverse operation and fundamental properties. A detailed analysis of RDTM’s methodology follows, highlighting its advantages in simplifying complex financial models. The study then focuses on transforming the governing model for ESCOM with MLPF into a standard heat-like equation. This critical transformation enables the application of RDTM to effectively solve the simplified equation. The process of deriving the standard heat like equation from the original ESCOM with MLPF is meticulously detailed, showcasing the method’s robustness and precision. RDTM is applied to solve the standard heat-like equation, resulting in a valuation formula for ESCOM with MLPF. This formula serves as a practical tool for financial analysts and researchers in option pricing. The study includes an extensive evaluation of RDTM’s suitability, effectiveness and accuracy in solving ESCOM with MLPF by testing various selected parameters against the fundamental analytical formula. The results demonstrate the method’s reliability and precision. In conclusion, this work underscores RDTM’s potential as a powerful and versatile tool for financial modeling and option pricing. The findings indicate that RDTM simplifies the computational process and enhances the accuracy of solutions, making it an asset for financial analysts and researchers.