We apply a physics-informed deep-learning approach the PINN approach to the Black-Scholes equation for pricing American and European options. We test our approach on both simulated as well as real market data, compare it to analytical/numerical benchmarks. Our model is able to accurately capture the price behaviour on simulation data, while also exhibiting reasonable performance for market data. We also experiment with the architecture and learning process of our PINN model to provide more understanding of convergence and stability issues that impact performance.

翻译：我们采用物理信息深度学习（PINN）方法，将Black-Scholes方程应用于美式和欧式期权的定价。我们在模拟数据及真实市场数据上测试了该方法，并与解析/数值基准进行了对比。该模型能精确捕捉模拟数据中的价格行为，同时在市场数据上展现出合理性能。我们还对PINN模型的架构与学习过程进行了实验，以深化对影响性能的收敛性与稳定性问题的理解。