Option Pricing of the Black–Scholes Equation: AStudy Using Physics-Informed and ArtificialNeural Networks
DOI:
https://doi.org/10.53799/9qpmy141Keywords:
Black–Scholes equation, Option pricing, ANN, PINNs, Adam optimizerAbstract
This study aims to carry out a comparative analysis of Artificial Neural Networks (ANN) and Physics-Informed Neural Networks (PINNs) in solving the Black-Scholes (BS) model for European call option pricing. PINNs have gained prominence in various engineering and financial fields due to their effectiveness in solving practical applications. In the last two decades, researchers have attempted to resolve BS model using numerical techniques; nevertheless, the difficulty of mesh generation complicates the numerical solution, particularly when addressing complex geometry. To address the BS model using an ANN, we initially trained our ANN with empirical data to obtain weights and biases leading to a fairly accurate solution for the untrained data. But, while solving the BS model with PINNs, no preexisting data is needed; we trained our PINNs model with the initial and boundary conditions. We employ the backpropagation technique in conjunction with the Adam optimizer to reduce the error. This study demonstrates that PINNs yield more accurate results than ANNs and that the predictions made by PINNs fit well with the exact findings. Thus, we can employ the PINNs method in substitution of the conventional numerical method.References
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