Calibrating L\'evy Processes from Observations Based on Neural Networks and Automatic Differentiation
We propose a method for calibrating multivariate Levy processes from sample paths. We approximate the unknown Levy measure using neural networks and demonstrate that neural networks are superior due to their regularization effect in the presence of noise, compared to piecewise linear, radial basis function and direct methods. The approach allows easy implementation for both discretization and optimization thanks to automatic differentiation. We also derive the error bound for the estimation and identify different sources of errors. The analysis is demonstrated in the numerical experiments and an application in stock markets is also presented.