solving the black-scholes problem using a combined numerical method (a case study of tehran stock exchange)

The black-scholes model is one of the most widely used frameworks for pricing options in financial markets. however, its analytical solutions are often limited to idealized conditions, necessitating the use of numerical methods for more complex scenarios. this study proposes a combined numerical approach to solve the black-scholes equation, specifically focusing on call option pricing in the context of iran's financial market. the proposed method integrates fully implicit and explicit methods to enhance accuracy and computational efficiency. by applying this approach to historical data from the iranian options market, we demonstrate its effectiveness in capturing market dynamics and pricing call options under local conditions. the results indicate that the combined numerical method not only provides reliable pricing estimates but also offers insights into the unique characteristics of option trading in emerging markets like iran. this research contributes to the growing body of literature on numerical methods in financial engineering and provides practical tools for traders and analysts in developing economies.