Abstract
We propose a non-parametric stable calibration method based on Tikhonov regularization for the local speed function in a local Levy model. The jump term in this model introduces an integral operator into the classic Black-Scholes partial di erential equation such that the associated model calibration to observed option prices can be treated as a parameter identication problem for a partial integro-di erential 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.
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