  Quantization algorithms have been successfully adopted to option pricing in
finance thanks to the high convergence rate of the numerical approximation. In
particular, very recently, recursive marginal quantization has been proven to
be a flexible and versatile tool when applied to stochastic volatility
processes. In this paper we apply for the first time quantization 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 induced
approximation errors, and we describe in numerical examples practical tools for
fast vanilla and exotic option pricing.
