A semi-smooth Newton method for an inverse problem in option pricing

We present an optimal control approach using a Lagrangian framework to identify local volatility functions from given option prices. We employ a globalized sequential quadratic programming (SQP) algorithm and implement a line search strategy. The linear-quadratic optimal control problems in each iteration are solved by a primal-dual active set strategy which leads to a semi-smooth Newton method. We present first- and second-order analysis as well as numerical results.