In this article, we develop a systematic approach to the reduction of dimensionality of smile-enabled models by projecting them onto a displaced version of the two-dimensional Heston process. The projection is the key for deriving efficient, analytical approximations to European option prices in such models. This is a further development of the method of Markovian projection previously used for projecting on the displaced-diffusion process (with skew but without smile). The method is derived in a generic form and has a wide range of suitable applications. Examples for spread and basket options are given.

Authors: A. Antonov, T. Misirpashaev, and V. Piterbarg