Before revision:  In this paper we apply for the first time these techniques to the family of polynomial processes, by exploiting , whenever possible, their peculiar properties. We derive theoretical results to assess the  approximation errors, and we describe in numerical examples practical tools for fast  exotic option pricing.
After revision:  In this paper we apply for the first time these techniques to the family of polynomial processes, by exploiting their peculiar nature. We focus our analysis on the stochastic volatility Jacobi process, by presenting two alternative quantization procedures: the first is a new discretization technique, whose foundation lies on the polynomial structure of the underlying process and which is suitable for vanilla option pricing, the second is based on recursive marginal quantization and it allows for pricing of (vanilla and) exotic derivatives. We prove theoretical results to assess the approximation errors, and we describe in numerical examples practical tools for fast exotic option pricing.