Markovian lifts of positive semidefinite affine Volterra-type processes

Christa Cuchiero () and Josef Teichmann
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Christa Cuchiero: Vienna University of Economics and Business
Josef Teichmann: ETH Zürich

Decisions in Economics and Finance, 2019, vol. 42, issue 2, No 5, 407-448

Abstract: Abstract 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.

Keywords: Stochastic partial differential equations; Affine processes; Wishart processes; Hawkes processes; Stochastic Volterra processes; Rough volatility models; 60H15; 60J25 (search for similar items in EconPapers)
JEL-codes: C G (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (28)

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DOI: 10.1007/s10203-019-00268-5

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