Modeling and pricing European options are crucial tasks for financial companies seeking to determine the fair value of these instruments. Conventional methods, such as using Black-Scholes partial differential equations (PDEs), face challenges due to the high complexity involved and lack of data. To address these challenges, PINNs have recently emerged as a promising approach to solving the Black-Scholes PDEs for European options. In this paper, we tackle the two-dimensional Black-Scholes model to determine the price of a European exchange option. We employ a kind of ANNs (PINN) that is specifically designed to learn the option’s value by minimizing an appropriately defined loss function. The data for our study were generated through simulations conducted in Python. Our results demonstrate the efficacy of the PINN approach by comparing the computed fair value of a European exchange option with the traditional solutions. The findings underscore the potential of PINNs in providing accurate and efficient pricing for complex financial derivatives.
Tavakoli et al. (Sun,) studied this question.