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December 2012 Functional relationships between price and volatility jumps and their consequences for discretely observed data
Jean Jacod, Claudia Klüppelberg, Gernot Müller
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J. Appl. Probab. 49(4): 901-914 (December 2012). DOI: 10.1239/jap/1354716647

Abstract

Many prominent continuous-time stochastic volatility models exhibit certain functional relationships between price jumps and volatility jumps. We show that stochastic volatility models like the Ornstein--Uhlenbeck and other continuous-time CARMA models as well as continuous-time GARCH and EGARCH models all exhibit such functional relations. We investigate the asymptotic behaviour of certain functionals of price and volatility processes for discrete observations of the price process on a grid, which are relevant for estimation and testing problems.

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Jean Jacod. Claudia Klüppelberg. Gernot Müller. "Functional relationships between price and volatility jumps and their consequences for discretely observed data." J. Appl. Probab. 49 (4) 901 - 914, December 2012. https://doi.org/10.1239/jap/1354716647

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1263.60038
MathSciNet: MR3058978
Digital Object Identifier: 10.1239/jap/1354716647

Subjects:
Primary: 60G48 , 60H30 , 91G70
Secondary: 62G10 , 62M02

Keywords: Barndorff-Nielsen Shephard model , CARMA , COGARCH , Common jumps , continuous-time GARCH , high-frequency data , Itô semimartingale , Lévy process , Ornstein--Uhlenbeck process , stochastic volatility

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 4 • December 2012
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