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

Loading...
Thumbnail Image
Date
2011
Volume
1631
Issue
Journal
Series Titel
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Link to publishers version
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 $X_Delta$ for some $Delta > 0$ 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 the convergence rates for the corresponding estimator and prove that these rates can not be improved in general.

Description
Keywords
Affine stochastic volatility model, Abelian theorem, Blumenthal-Getoor index
Citation
Belomestny, D., & Panov, V. (2011). Abelian theorems for stochastic volatility models with application to the estimation of jump activity of volatility (Vol. 1631). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Collections
License
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.