Quadratic optimal functional quantization of stochastic processes and numerical applications

TL;DR

This paper reviews recent advances in quadratic functional quantization of stochastic processes, focusing on computational methods and applications like option pricing, providing insights into approximating complex stochastic models efficiently.

Contribution

It offers a comprehensive overview of the quadratic functional quantization technique, highlighting new computational strategies and practical applications in finance.

Findings

Effective approximation of stochastic processes using quadratic quantization

Numerical methods for pricing path-dependent European options

Enhanced computational techniques for functional quantization

Abstract

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a Hilbert-valued random variable, using a nearest neighbour projection on a finite codebook. A special emphasis is made on the computational aspects and the numerical applications, in particular the pricing of some path-dependent European options.