Empirical Characteristic Function Method for Leverage Effect and Volatility of Volatility: Estimation and Feasible Inference

We develop jump-robust estimators of the leverage effect and volatility of volatility using high-frequency data. Our construction begins with a spot volatility estimator based on the empirical characteristic function of high-frequency increments. This method can mitigate the contamination from jumps, which can be of infinite variation. We then construct estimators of the leverage effect and volatility of volatility and correct for the bias induced by spot volatility estimation. We establish consistency and central limit theorems under conditions that allow greater jump activity than existing methods. We also develop consistent estimators of the asymptotic variances, making the limiting results feasible for statistical inference. Simulation studies demonstrate the improved finite-sample performance of the proposed estimators, particularly in the presence of infinite variation jumps. An empirical application provides evidence of nonzero leverage effect and volatility of volatility, when the jump activity is intensive.