Affine Volterra processes

Abstract : 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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Submitted on : Thursday, August 8, 2019 - 5:55:00 PM
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  • HAL Id : hal-01580801, version 2
  • ARXIV : 1708.08796

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Eduardo Abi Jaber, Martin Larsson, Sergio Pulido. Affine Volterra processes. 2019. ⟨hal-01580801v2⟩

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