Files and links (1)
Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
Efficient Volatility Estimation for L vy Processes with Jumps of Unbounded Variation
01 Jan 2022
Abstract
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic variation of the continuous component of an It semimartingale with jumps. Several rate- and variance-efficient estimators have been proposed in the literature when the jump component is of bounded variation. However, to date, very few methods can deal with jumps of unbounded variation. By developing new high-order expansions of the truncated moments of a L vy process, we construct a new rate- and variance-efficient estimator for a class of L vy processes of unbounded variation, whose small jumps behave like those of a stable L vy process with Blumenthal-Getoor index less than $8/5$. The proposed method is based on a two-step debiasing procedure for the truncated realized quadratic variation of the process. Our Monte Carlo experiments indicate that the method outperforms other efficient alternatives in the literature in the setting covered by our theoretical framework.
40 pages
Metrics
10 Record Views
Details
- Title
- Efficient Volatility Estimation for L vy Processes with Jumps of Unbounded Variation
- Creators
- B. Cooper BonieceJos E. Figueroa-L pezYuchen Han
- Publisher
- arXiv
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862312804721