Estimation of the Continuous and Discontinuous Leverage Effects

ABSTRACT 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.

[1]  I. Curato.  Estimation of the Stochastic Leverage Effect Using the Fourier Transform Method , 2015, Stochastic Processes and their Applications.

[2]  R. Laeven,et al.  Testing for self-excitation in jumps , 2018 .

[3]  George Tauchen,et al.  Adaptive estimation of continuous-time regression models using high-frequency data , 2017 .

[4]  H. Thompson,et al.  High-Frequency Financial Econometrics , 2016 .

[5]  Dacheng Xiu,et al.  Generalized Method of Integrated Moments for High-Frequency Data , 2015 .

[6]  Oleg Bondarenko,et al.  Exploring Return Dynamics via Corridor Implied Volatility , 2015 .

[7]  S. Sanfelici,et al.  Measuring the Leverage Effect in a High-Frequency Trading Framework , 2015 .

[8]  J. Jacod,et al.  High-Frequency Financial Econometrics , 2014 .

[9]  P. Mykland,et al.  The Estimation of Leverage Effect With High-Frequency Data , 2013 .

[10]  D. Xiu,et al.  Spot Variance Regressions , 2013 .

[11]  Jean Jacod,et al.  Quarticity and other functionals of volatility: Efficient estimation , 2012, 1207.3757.

[12]  Estimation of Correlation for Continuous Semimartingales , 2012 .

[13]  Michael Sørensen,et al.  Estimating functions for diffusion-type processes , 2012 .

[14]  Mathias Vetter,et al.  Nonparametric inference on Lévy measures and copulas , 2012, 1205.0417.

[15]  Jianqing Fan,et al.  Journal of the American Statistical Association Estimating False Discovery Proportion under Arbitrary Covariance Dependence Estimating False Discovery Proportion under Arbitrary Covariance Dependence , 2022 .

[16]  Dan Wang.  Estimation of Leverage Effect , 2012 .

[17]  Mathias Vetter,et al.  Estimation of integrated volatility of volatility with applications to goodness-of-fit testing , 2011, 1206.5761.

[18]  Jianqing Fan,et al.  The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency , 2011 .

[19]  Jean Jacod,et al.  Discretization of Processes , 2011 .

[20]  Jasmina Hasanhodzic,et al.  Black's Leverage Effect is not Due to Leverage , 2011 .

[21]  M. B. Rajarshi.  Statistical Inference for Stochastic Processes , 2011, International Encyclopedia of Statistical Science.

[22]  Jean Jacod,et al.  Do price and volatility jump together , 2010, 1010.4990.

[23]  F. Bandi,et al.  Time-Varying Leverage Effects , 2010 .

[24]  Yacine Ait-Sahalia,et al.  Modeling Financial Contagion Using Mutually Exciting Jump Processes , 2010 .

[25]  R. Laeven.  Modeling financial contagion , 2010 .

[26]  Almut E. D. Veraart,et al.  Stochastic volatility and stochastic leverage , 2009 .

[27]  Yingying Fan,et al.  Testing and Detecting Jumps Based on a Discretely Observed Process , 2008 .

[28]  Fabien Panloup,et al.  Estimation of the instantaneous volatility , 2008, 0812.3538.

[29]  Jean Jacod,et al.  Limit Theorems for Moving Averages of Discretized Processes Plus Noise , 2008, 1010.0335.

[30]  Jianqing Fan,et al.  Spot volatility estimation for high-frequency data ∗ , 2008 .

[31]  Jean Jacod,et al.  Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9 , 2007 .

[32]  J. Jacod,et al.  Testing for Jumps in a Discretely Observed Process , 2009, 0903.0226.

[33]  Jean Jacod,et al.  Asymptotic properties of realized power variations and related functionals of semimartingales , 2006, math/0604450.

[34]  T. Bollerslev,et al.  Leverage and Volatility Feedback Effects in High-Frequency Data , 2005 .

[35]  Jun Yu.  On Leverage in a Stochastic Volatility Model , 2004 .

[36]  Nicholas G. Polson,et al.  The Impact of Jumps in Volatility and Returns , 2000 .

[37]  Stephen Figlewski,et al.  Is the "Leverage Effect" a Leverage Effect? , 2000 .

[38]  Guojun Wu,et al.  Asymmetric Volatility and Risk in Equity Markets , 1997 .

[39]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[40]  John Y. Campbell,et al.  No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns , 1991 .

[41]  K. French,et al.  Expected stock returns and volatility , 1987 .

[42]  R. Pindyck.  Risk, Inflation, and the Stock Market , 1983 .

[43]  A. Christie,et al.  The stochastic behavior of common stock variances: value , 1982 .