B. Cooper Boniece, José E. Figueroa-López, Yuchen Han
arXiv 21 Sep 2022 · Econometrics · publishedStochastic Processes and their Applications (2024) · 2 citations (OpenAlex)
arXiv:2209.10128 · PDF · DOI · OpenAlex · Extracted main text
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems has been the estimation of the quadratic variation of the continuous component of an It\^o 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 locally stable L\'evy process, we propose a new rate- and variance-efficient volatility estimator for a class of It\^o semimartingales whose jumps behave locally like those of a stable L\'evy process with Blumenthal-Getoor index $Y\in (1,8/5)$ (hence, of unbounded variation). The proposed method is based on a two-step debiasing procedure for the truncated realized quadratic variation of the process and can also cover the case $Y<1$. Our Monte Carlo experiments indicate that the method outperforms other efficient alternatives in the literature in the setting covered by our theoretical framework.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | J. Jacod, V. Todorov (2014) Efficient estimation of integrated volatility in presence of infinite variation jumps | 1.000 | 26 | 4 | 100% |
| 2 | F. Mies (2020) Rate-optimal estimation of the blumenthal–getoor index of a Lévy process | 1.000 | 15 | 3 | 100% |
| 3 | J. E. Figueroa-López, S. Ólafsson (2016) Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps | 0.811 | 4 | 2 | 100% |
| 4 | J. E. Figueroa-López, R. Gong, C. Houdré (2016) High-order short-time expansions for ATM option prices of exponential Lévy models | 0.737 | 4 | 3 | 50% |
| 5 | P. Carr, H. Geman, D. B. Madan, M. Yor (2002) The fine structure of asset returns: An empirical investigation | 0.644 | 2 | 2 | 100% |
| 6 | J. Jacod, M. Reiss (2014) A remark on the rates of convergence for integrated volatility estimation in the presence of jumps | 0.644 | 2 | 2 | 100% |
| 7 | J. E. Figueroa-López, R. Gong, Y. Han (2022) Estimation of tempered stable Lévy models of infinite variation | 0.613 | 13 | 4 | 23% |
| 8 | K.-i. Sato, Lévy Processes and Infinitely Divisible Distributions, n… (1999) | 0.585 | 3 | 3 | 33% |
| 9 | Y. Aït-Sahalia, J. Jacod (2009) Estimating the degree of activity of jumps in high frequency data | 0.511 | 3 | 2 | 33% |
| 10 | C. Amorino, A. Gloter (2020) Unbiased truncated quadratic variation for volatility estimation in jump diffusion processes | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 29 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Debiased Kernel Estimation of Spot Volatility in the Presence of Infinite Variation Jumps | 0.597 | 47 | 5 |