Markovian lifts of positive semidefinite affine Volterra-type processes

Cuchiero, Christa and Teichmann, Josef (2019) Markovian lifts of positive semidefinite affine Volterra-type processes. Decisions in Economics and Finance, 42. pp. 407-448. ISSN 1129-6569

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We consider stochastic partial differential equations appearing as Markovian lifts of matrix-valued (affine) Volterra-type processes from the point of view of the generalized Feller property (see, e.g., Dörsek and Teichmann in A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). We introduce in particular Volterra Wishart processes with fractional kernels and values in the cone of positive semidefinite matrices. They are constructed from matrix products of infinite dimensional Ornstein–Uhlenbeck processes whose state space is the set of matrix-valued measures. Parallel to that we also consider positive definite Volterra pure jump processes, giving rise to multivariate Hawkes-type processes. We apply these affine covariance processes for multivariate (rough) volatility modeling and introduce a (rough) multivariate Volterra Heston-type model.

Item Type: Article
Additional Information: The authors are grateful for the support of the ETH Foundation and Erwin Schrödinger Institut Wien. Christa Cuchiero gratefully acknowledges financial support by the Vienna Science and Technology Fund (WWTF) under Grant MA16-021.
Keywords: Stochastic partial differential equations, Affine processes, Wishart processes, Hawkes processes, Stochastic Volterra processes, Rough volatility models
Classification Codes: MSC 60H15 60J25; JEL C.5, G.1
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Version of the Document: Published
Depositing User: ePub Administrator
Date Deposited: 25 Oct 2019 14:45
Last Modified: 12 Aug 2020 15:27
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