Markovian structure of the Volterra Heston model

Understand

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.