Gradient Computation for Model Calibration with Pointwise Observations

Mathematical models for option pricing often result in partial differential equations of parabolic type. The calibration of these models leads to an optimization problem with PDE constraints and usually pointwise observations in the objective function. Thus, the adjoint equation of this problem involves Dirac delta functions and needs a special treatment from a numerical point of view. We show by means of numerical results that also the order of discretizing and optimizing plays an important role.

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