On the estimation of leverage effect and volatility of volatility in the presence of jumps

TL;DR

This paper develops robust estimators for leverage effect and volatility of volatility using high-frequency data with jumps, outperforming existing methods especially with infinite variation jumps, and applies them to real market data.

Contribution

It introduces a new empirical characteristic function-based estimator that handles general jumps, with proven asymptotic properties and superior performance in simulations.

Findings

Estimators are asymptotically normal and consistent.

Proposed method outperforms existing estimators, especially with infinite variation jumps.

Application reveals nonzero leverage effect and volatility of volatility in real data.

Abstract

We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the high-frequency increments to deal with the effect of jumps, based on which the estimators of leverage effect and volatility of volatility are proposed. Compared with existing estimators, our method is valid under more general jumps, making it a better alternative for empirical applications. Under some mild conditions, the asymptotic normality of the estimators is established and consistent estimators of the limiting variances are proposed based on the estimation of volatility functionals. We conduct extensive simulation study to verify the theoretical results. The results demonstrate that our estimators have relative better performance than the existing ones, especially when the jump is of infinite variation. Besides, we apply our estimators to a real high-frequency dataset, which reveals nonzero leverage effect and volatility of volatility in the market.