Option Pricing and Local Volatility Surface by Physics-Informed Neural Network

We use an artificial neural network for finance in two directions: to estimate prices and Greeks based on the geometric Brownian motion and the constant elasticity of variance model for European options, and to construct a local volatility surface. To show the efficiency and successful usage of the network, we compare prices and Greeks obtained by a solution formula and by the artificial neural network when there is a solution formula is known. Then, we calculate Dupire’s equations to construct a local volatility surface by the network.