We propose a non-parametric stable calibration method based on Tikhonov regularization for the local speed function in a local L´evy model. The jump term in this model introduces an integral operator into the classic BlackScholes partial differential equation such that the associated model calibration to observed option prices can be treated as a parameter identification problem for a partial integrodifferential equation. This problem is shown to be ill-posed and thus requires regularization. It is proven that nonlinear Tikhonov regularization is a stable and convergent method for this problem. Furthermore, convergence rate results are established under an abstract source condition. Finally the theoretical results are underpinned by numerical illustrations including a real-world example.