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On the estimation of leverage effect and volatility of volatility in the presence of jumps

Qiang Liu, Zhi Liu, Wang Zhou

arXiv 2 Nov 2025 · Statistics — Methodology

arXiv:2511.00944 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the high-frequency increments to deal with the effect of jumps, based on which the estimators of leverage effect and volatility of volatility are proposed. Compared with existing estimators, our method is valid under more general jumps, making it a better alternative for empirical applications. Under some mild conditions, the asymptotic normality of the estimators is established and consistent estimators of the limiting variances are proposed based on the estimation of volatility functionals. We conduct extensive simulation study to verify the theoretical results. The results demonstrate that our estimators have relative better performance than the existing ones, especially when the jump is of infinite variation. Besides, we apply our estimators to a real high-frequency dataset, which reveals nonzero leverage effect and volatility of volatility in the market.

Citation extraction

35
references
123
in-text mentions
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distinct cited
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self-citations
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appendix boundary found by appendix_titled_section at “Appendix: Proofs” · 33% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Y. Aït-Sahalia and J. Jacod (2014) High-Frequency Financial Econometrics1.000113100%
2Wang, Christina D and Mykland, Per A (2014) The estimation of leverage effect with high-frequency data1.00083100%
3Vetter, Mathias (2015) Estimation of integrated volatility of volatility with applications to goodness-of-fit testing1.00053100%
4Jean Jacod and Viktor Todorov (2014) Efficient Estimation of Integrated Volatility in Presence of Infinite Variation Jumps0.9619689%
5A\"it-Sahalia, Yacine and Fan, Jianqing and Laeven, Roger JA and Wan… (2017) Estimation of the continuous and discontinuous leverage effects0.94112483%
6Liu, Qiang and Liu, Yiqi and Liu, Zhi (2018) Estimating spot volatility in the presence of infinite variation jumps self0.86225564%
7Kalnina, Ilze and Xiu, Dacheng (2017) Nonparametric estimation of the leverage effect: A trade-off between robustness and efficiency0.84333100%
8Barndorff-Nielsen, Ole E and Veraart, Almut (2009) Stochastic volatility of volatility in continuous time0.73732100%
9Jing, B. Y and Kong, X. B. and Liu, Z. and Mykland, P. A (2012) On the jump activity index for semimartingales self0.73732100%
10Jacod, J. and Protter, P (2012) Discretization of Processes0.6939333%

Showing the top 10 of 35 scored citations.