Abelian theorems for stochastic volatility models with application to the estimation of jump activity

Denis Belomestny and Vladimir Panov

Stochastic Processes and their Applications, 2013, vol. 123, issue 1, 15-44

Abstract: In this paper, we prove a kind of Abelian theorem for a class of stochastic volatility models (X,V) where both the state process X and the volatility process V may have jumps. Our results relate the asymptotic behavior of the characteristic function of XΔ for some Δ>0 in a stationary regime to the Blumenthal–Getoor indexes of the Lévy processes driving the jumps in X and V. The results obtained are used to construct consistent estimators for the above Blumenthal–Getoor indexes based on low-frequency observations of the state process X. We derive convergence rates for the corresponding estimator and show that these rates cannot be improved in general.

Keywords: Affine stochastic volatility model; Abelian theorem; Blumenthal–Getoor index (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:1:p:15-44

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DOI: 10.1016/j.spa.2012.08.015

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