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

2025-11-02

AI Summary

This paper addresses the robust estimation of the leverage effect and volatility-of-volatility (vol-of-vol) for high-frequency financial data contaminated by jumps. We propose a novel instantaneous volatility estimator based on the empirical characteristic function of high-frequency increments, which—uniquely among existing approaches—imposes no restrictions on jump activity (e.g., finite or infinite variation), thereby achieving both theoretical rigor and empirical applicability. By constructing an asymptotically normal functional estimator of volatility and developing a consistent variance estimation strategy, we ensure reliable statistical inference. Monte Carlo simulations demonstrate that our estimator significantly outperforms state-of-the-art alternatives in both accuracy and robustness. Empirical analysis of Chinese and U.S. equity markets confirms statistically significant, non-zero leverage effects and vol-of-vol, underscoring the economic relevance of these higher-order volatility features.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Estimating leverage effect and volatility of volatility with jumps
• Developing improved estimators using high-frequency financial data
• Addressing limitations of existing methods under general jump conditions

Innovation

• Estimates leverage effect using high-frequency data
• Constructs spot volatility estimator via characteristic function
• Handles infinite variation jumps better than alternatives