Stationary covariance regime for affine stochastic covariance models in Hilbert spaces

Martin Friesen and Sven Karbach ()
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Martin Friesen: Dublin City University
Sven Karbach: University of Amsterdam

Finance and Stochastics, 2024, vol. 28, issue 4, No 5, 1077-1116

Abstract: Abstract This paper introduces stochastic covariance models in Hilbert spaces with stationary affine instantaneous covariance processes. We explore the applications of these models in the context of forward curve dynamics within fixed-income and commodity markets. The affine instantaneous covariance process is defined on positive self-adjoint Hilbert–Schmidt operators, and we prove the existence of a unique limit distribution for subcritical affine processes, provide convergence rates of the transition kernels in the Wasserstein distance of order p ∈ [ 1 , 2 ] $p \in [1,2]$ , and give explicit formulas for the first two moments of the limit distribution. Our results allow us to introduce affine stochastic covariance models in the stationary covariance regime and to investigate the behaviour of the implied forward volatility for large forward dates in commodity forward markets.

Keywords: Affine processes; Invariant measure; Stationarity; Ergodicity; Stochastic covariance; Implied forward volatility; Generalised Feller semigroups; 60J25; 37A25; 60G10 (search for similar items in EconPapers)
JEL-codes: C60 G12 G13 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00780-024-00543-3

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