Markovian structure of the Volterra Heston model

Eduardo Abi Jaber (1) , Omar El Euch (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 X - École polytechnique

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.

Mots clés: Affine Volterra processes; stochastic Volterra equations; Markovian representation; stochastic invariance; Riccati-Volterra equations; rough volatility

Domaines: Probabilités [math.PR]; Finance quantitative [q-fin.CP]

Eduardo Abi Jaber, Omar El Euch. Markovian structure of the Volterra Heston model. 2018. ⟨hal-01716696v1⟩