Markovian projection for volatility calibration

European-style options are usually the most liquid options available in any market. More often than not, they are the only options that are liquid enough to be used for model calibration. Thus, efficient methods for valuing European-style options are a critical requirement for any model. In this article, we develop the Markovian projection method, a very general and powerful approach for deriving accurate approximations of European-style option prices in a wide range of models. Various ideas