The tangential cone condition for the iterative calibration of local volatility surfaces

In this paper, we prove that the parameter-to-solution map associated to the inverse problem of determining the diffusion coefficient in a parabolic partial differential equation satisfies the local tangential cone condition. In particular, we show stability and convergence of the regularized solutions by means of Landweber iteration. Our result has an immediate application to the local volatility calibration problem of the Black-Scholes model for European call options. We present a numerical validation based on simulated data to this calibration problem and discuss the results. We also prove convergence and stability of Kaczmarz-type strategies of the local volatility calibration problem by transforming the problem into a system of non-linear ill-posed equations.