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Markovian structure of the Volterra Heston model

Eduardo Abi jaber () and Omar El Euch ()
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Eduardo Abi jaber: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique
Omar El Euch: X - École polytechnique

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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: Markovian representation; stochastic Volterra equations; Affine Volterra processes; stochastic invariance; Riccati-Volterra equations; rough volatility (search for similar items in EconPapers)
Date: 2018-02-28
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01716696v2
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