Fizik temelli sinir ağı tabanlı opsiyon fiyatlaması

Option pricing is an important problem in finance. The most common option pricing methodologies are Black-Scholes, CEV, Heston, and SABR, where all of them can be described by Partial Differential Equations. On the other hand, as a deep learning technique, Physics-Informed Neural Networks~(PINNs) have shown great potential in providing approximate solutions to Partial Differential Equations~(PDEs). In this study, we come up with Physics-Informed Neural Network-based option pricing methods under these 4 pricing models. We evaluate our method using both simulated and actual market data, and assess its performance against analytical and numerical reference models. The empirical results for index options such as RUT and SPX, as well as index constituent companies options, show that the proposed deep learning models have lower absolute errors than the classical Black–Scholes model solution. Our proposed solution also performs better than the recently proposed PINNsFormer for the option pricing task. Our results on both European and American options show the potential importance of Physics-Informed Neural Networks in solving option pricing, which can also be extended to other financial asset pricing problems. Our methods, analysis code, and datasets are available at: https://github.com/seferlab/PINN_for_Options