The Numerical Solution of American Option Pricing Problem

In this paper, we study the neural network algorithm for American option pricing by the time series difference method and residual network. Essentially, it is a kind of high-dimensional parabolic partial differential equation with reflection obstacles, and it is equivalently expressed as a backward stochastic differential equation with reflection (RBSDE) by the Feynman-Kac formula. In the numerical experiment of RBSDE, we analyze the experimental results under different parameters. The numerical solution in the low-dimensional case is compared with the results of the traditional binary tree method, which verifies the effectiveness and reliability of the algorithm in this paper. On this basis, we further study the high-dimensional problem.