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Pré-Publication, Document De Travail Année : 2017

Affine Volterra processes

Résumé

We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are neither semimartingales, nor Markov processes in general. We provide explicit exponential-affine representations of the Fourier--Laplace functional in terms of the solution of an associated system of deterministic integral equations, extending well-known formulas for classical affine diffusions. For specific state spaces, we prove existence, uniqueness, and invariance properties of solutions of the corresponding stochastic convolution equations. Our arguments avoid infinite-dimensional stochastic analysis as well as stochastic integration with respect to non-semimartingales, relying instead on tools from the theory of finite-dimensional deterministic convolution equations. Our findings generalize and simplify recent results in the literature on rough volatility models in finance.
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Dates et versions

hal-01580801 , version 1 (02-09-2017)
hal-01580801 , version 2 (08-08-2019)

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Eduardo Abi Jaber, Martin Larsson, Sergio Pulido. Affine Volterra processes. 2017. ⟨hal-01580801v1⟩
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