The price-leverage covariation as a measure of the response of the leverage effect to price and volatility changes

We study the sensitivity of the leverage effect to changes of the volatility and the price, showing the existence of an analytical link between the latter and the price-leverage covariation in settings with, respectively, stochastic and level-dependent volatility. From the financial standpoint, the results we obtain allow for the interpretation of the price-leverage covariation as a gauge of the responsiveness of the leverage effect to price and volatility changes. The empirical study of S&P500 high-frequency prices over the period March 2018-April 2018, carried out by means of nonparametric Fourier estimators, supports this interpretation of the role of the price-leverage covariation.