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 language | English |
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Pages (from-to) | 901-914 |
Number of pages | 14 |
Journal | Journal of Applied Probability |
Volume | 49 |
Issue number | 4 |
DOIs | |
State | Published - 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