Local volatility calibration with optimal control in a Lagrangian framework

We develop a Lagrangian based method for solving the calibration problem of identifying a local volatility function that makes the solution to Dupire's pricing equation match observed market quotes on options. Our method uses well established techniques from the field of inverse problems, but differs from other published methods in that our formulation makes it possible to use a Newton method with the analytic Jacobian of the system corresponding to first order optimality conditions of our problem. We give a numerical example with market data of options on the Euro Stoxx 50 index and find that our method is efficient and robust in its ability to identify a volatility function that fit observed data.QC 20170911