Journal article

Publication year: 2022

Pages: 250-279

Journal: Stochastic Processes and their Applications

Volume number: 150

ISSN: 0304-4149

eISSN: 1879-209X

Open access status: Green

DOI Link: https://doi.org/10.1016/j.spa.2022.04.011

Publisher: Elsevier

Abstract: 
We extend recent results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions of Volterra equations driven by a Brownian motion with an inhomogeneous kernel K(t, s) and inhomogeneous drift and diffusion coefficients b(s, X-s) and sigma(s, X-s). In the case of affine b and sigma sigma(T) we show how the conditional Fourier-Laplace functional can be represented by a solution of an inhomogeneous Riccati-Volterra integral equation. For a kernel of convolution type K(t, s) = K(t - s) we establish existence of a solution to the stochastic inhomogeneous Volterra equation. If in addition b and sigma sigma(T) are affine, we prove that the conditional Fourier-Laplace functional is exponential-affine in the past path. Finally, we apply these results to an inhomogeneous extension of the rough Heston model used in mathematical finance. (C) 2022 Elsevier B.V. All rights reserved.

Harvard Citation style: Ackermann, J., Kruse, T. and Overbeck, L. (2022) Inhomogeneous affine Volterra processes, Stochastic Processes and their Applications, 150, pp. 250-279. https://doi.org/10.1016/j.spa.2022.04.011

APA Citation style: Ackermann, J., Kruse, T., & Overbeck, L. (2022). Inhomogeneous affine Volterra processes. Stochastic Processes and their Applications. 150, 250-279. https://doi.org/10.1016/j.spa.2022.04.011