Functional relationships between price and volatility jumps and their consequences for discretely observed data

Jean Jacod, Claudia Klüppelberg, Gernot Müller

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Many prominent continuous-time stochastic volatility models exhibit certain functional relationships between price jumps and volatility jumps. We showthat 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.

Original languageEnglish
Pages (from-to)901-914
Number of pages14
JournalJournal of Applied Probability
Volume49
Issue number4
DOIs
StatePublished - Dec 2012

Keywords

  • Barndorff-Nielsen Shephard model
  • CARMA
  • COGARCH
  • Common jumps
  • Continuous-time GARCH
  • High-frequency data
  • Itô semimartingale
  • Lévy process
  • Ornstein-Uhlenbeck process
  • Stochastic volatility

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