Markovian structure of the Volterra Heston model

Eduardo Abi Jaber; Omar El Euch

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arXiv · 1803.00477

Markovian structure of the Volterra Heston model

Eduardo Abi Jaber·Omar El Euch

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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.

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Eduardo Abi Jaber, Omar El Euch. 2018-03-01. Markovian structure of the Volterra Heston model. https://arxiv.org/abs/1803.00477

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