Model Calibration in Option Pricing

Abstract

We consider calibration problems for models of pricing derivatives which occur in mathematical finance. We discuss various approaches such as using stochastic differential equations or partial differential equations for the modeling process. We discuss the development in the past literature and give an outlook into modern approaches of modelling. Furthermore, we address important numerical issues in the valuation of options and likewise the calibration of these models. This leads to interesting problems in optimization, where, e.g., the use of adjoint equations or the choice of the parametrization for the model parameters play an important role.

Keywords

• Adjoints, Calibration, Jump models, Local volatility models, Mixed models, Partial differential equation (PDE), Stochastic differential equation (SDE), Stochastic volatility models.