Option Pricing and Local Volatility Surface by Physics-Informed Neural Network - Bae, Hyeong Ohk; Kang, Seunggu; Lee, Muhyun (Computational Economics, 2024)
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.
Keywords: 68T07; 91G20; Artificial neural network; Black–Scholes equation (BSE); C63; Constant elasticity of variance (CEV); G13; Option pricing, Local volatility; Physics-informed neural network (PINN)