Estimation of the Leverage Effect in Jump Processes

• Activity Number: 132
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Dan Christina Wang*+
• Companies: Princeton University
• Keywords: Leverage effect ; Semimartingale ; consistency ; jumps ; microstructure noise ; nonparametric

Abstract

The leverage effect describes the (usually) negative correlation between stock returns and volatility. By defining the leverage effect parameter as the quadratic covariation between the log price and volatility processes, we studied the nonparametric estimation of the leverage effect when jumps present in both log price and volatility processes. In this case, the leverage effect contains a continuous and a discontinuous components. we proposed consistent estimators for the continuous and discontinuous components of the leverage effect respectively, and also the combined leverage effect. We also provided central limit theorems for the leverage effect estimators and the simulation results which corroborate the theoretical finding. We further considered the estimation when market microstructure noise presents in the log price process, and provided the consistent estimators of the leverage effect. With E-mini S&P 500 futures, we applied the estimators to hypothesis testing and found positive evidence of the presence of the leverage effect discontinuous component, and to estimating the correlation coefficients of log price and its own volatility, showing the time varying properties.