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Markovian structure of the Volterra Heston model

Abi Jaber, Eduardo; El Euch, Omar (2019), Markovian structure of the Volterra Heston model, Statistics & Probability Letters, 69, p. 63-72. 10.1016/j.spl.2019.01.024

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AJEE_Markovian_Final_20180223.pdf (311.7Kb)
Type
Article accepté pour publication ou publié
Date
2019
Journal name
Statistics & Probability Letters
Volume
69
Publisher
Elsevier
Pages
63-72
Publication identifier
10.1016/j.spl.2019.01.024
Metadata
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Author(s)
Abi Jaber, Eduardo
El Euch, Omar
Abstract (EN)
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.
Subjects / Keywords
Markovian representation; stochastic Volterra equations; Affine Volterra processes; stochastic invariance; Riccati-Volterra equations; rough volatility

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