Estimation of the Continuous and Discontinuous Leverage Effects

Yacine Aït-Sahalia, Jianqing Fan, Roger J.A. Laeven, Christina Dan Wang, Xiye Yang

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


This article examines the leverage effect, or the generally negative covariation between asset returns and their changes in volatility, under a general setup that allows the log-price and volatility processes to be Itô semimartingales. We decompose the leverage effect into continuous and discontinuous parts and develop statistical methods to estimate them. We establish the asymptotic properties of these estimators. We also extend our methods and results (for the continuous leverage) to the situation where there is market microstructure noise in the observed returns. We show in Monte Carlo simulations that our estimators have good finite sample performance. When applying our methods to real data, our empirical results provide convincing evidence of the presence of the two leverage effects, especially the discontinuous one. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1744-1758
Number of pages15
JournalJournal of the American Statistical Association
Issue number520
StatePublished - Oct 2 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Co-jumps
  • High-frequency data
  • Integrated volatility
  • Jumps
  • Market microstructure noise
  • Spot volatility


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