Robustness of Hilbert space-valued stochastic volatility models

Fred Espen Benth () and Heidar Eyjolfsson ()
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Fred Espen Benth: University of Oslo
Heidar Eyjolfsson: Reykjavik University

Finance and Stochastics, 2024, vol. 28, issue 4, No 6, 1117-1146

Abstract: Abstract In this paper, we show that Hilbert space-valued stochastic models are robust with respect to perturbations, due to measurement or approximation errors, in the underlying volatility process. Within the class of stochastic-volatility-modulated Ornstein–Uhlenbeck processes, we quantify the error induced by the volatility in terms of perturbations in the parameters of the volatility process. We moreover study the robustness of the volatility process itself with respect to finite-dimensional approximations of the driving compound Poisson process and semigroup generator, respectively, when considering operator-valued Barndorff-Nielsen and Shephard stochastic volatility models. We also give results on square root approximations. In all cases, we provide explicit bounds for the induced error in terms of the approximation of the underlying parameter. We discuss some applications to robustness of prices of options on forwards and volatility.

Keywords: Hilbert space-valued stochastic volatility; Robustness under perturbation; Stochastic-volatility-modulated Ornstein–Uhlenbeck processes; Robustness of options on forwards and volatility; 60H15; 60H25; 47B02 (search for similar items in EconPapers)
JEL-codes: C63 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/s00780-024-00542-4

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