Logo image
Back
Efficient integrated volatility estimation in the presence of infinite variation jumps via debiased truncated realized variations
Journal article   Open access   Peer reviewed

Efficient integrated volatility estimation in the presence of infinite variation jumps via debiased truncated realized variations

B. Cooper Boniece, José E. Figueroa-López and Yuchen Han
Stochastic processes and their applications, v 176, 104429
Oct 2024
DOI: https://doi.org/10.1016/j.spa.2024.104429
Featured in Collection :   UN Sustainable Development Goals @ Drexel
url
https://arxiv.org/abs/2209.10128View
SubmittedarXiv.org - Non-exclusive license to distribute,  Open
url
https://doi.org/10.1016/j.spa.2024.104429View
Published, Version of Record (VoR) Open

Abstract

Efficiency High-frequency data Integrated volatility estimation Itô semimartingale Truncated realized variations
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 Itô 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 Lévy process, we propose a new rate- and variance-efficient volatility estimator for a class of Itô semimartingales whose jumps behave locally like those of a stable Lévy process with Blumenthal–Getoor index Y∈(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.

Metrics

10 Record Views
2 citations in Web of Science

Details

UN Sustainable Development Goals (SDGs)

This publication has contributed to the advancement of the following goals:

#8 Decent Work and Economic Growth

InCites Highlights

Data related to this publication, from InCites Benchmarking & Analytics tool:

Collaboration types
Domestic collaboration
Web of Science research areas
Statistics & Probability
Logo image