Markovian structure of the Volterra Heston model
Probability
2018-03-02 v1
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.
Keywords
Cite
@article{arxiv.1803.00477,
title = {Markovian structure of the Volterra Heston model},
author = {Eduardo Abi Jaber and Omar El Euch},
journal= {arXiv preprint arXiv:1803.00477},
year = {2018}
}