Quantization goes Polynomial

TL;DR

This paper introduces novel quantization methods tailored for polynomial processes in finance, specifically for stochastic volatility Jacobi processes, enabling efficient pricing of vanilla and exotic options with theoretical error bounds.

Contribution

It pioneers the application of quantization techniques to polynomial processes, developing two new discretization methods suited for vanilla and exotic option pricing.

Findings

New discretization technique based on polynomial structure

Recursive marginal quantization applied to exotic derivatives

Theoretical error bounds for quantization approximations

Abstract

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.