Markovian structure of the Volterra Heston model

TL;DR

This paper characterizes the Markovian and affine properties of the Volterra Heston model using an infinite-dimensional framework, providing new insights into its structure and solutions.

Contribution

It introduces an infinite-dimensional adjusted forward process for the Volterra Heston model, establishing its stochastic PDE form and affine characteristic functional.

Findings

Proves the existence and uniqueness of a Banach-space valued square-root process.

Provides a new representation of the Volterra Heston model via an infinite system of affine diffusions.

Derives the Fourier-Laplace transform for the model.

Abstract

We characterize the Markovian and affine structure of the Volterra Heston model in terms of an infinite-dimensional adjusted forward process and specify its state space. More precisely, we show that it satisfies a stochastic partial differential equation and displays an exponentially-affine characteristic functional. As an application, we deduce an existence and uniqueness result for a Banach-space valued square-root process and provide its state space. This leads to another representation of the Volterra Heston model together with its Fourier-Laplace transform in terms of this possibly infinite system of affine diffusions.