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.

翻译：本研究探讨了在跳跃存在的情况下利用高频数据估计杠杆效应与波动率波动率的问题。我们首先通过使用高频增量的经验特征函数构建了即期波动率估计量，以处理跳跃的影响，并在此基础上提出了杠杆效应与波动率波动率的估计量。与现有估计量相比，我们的方法在更一般的跳跃条件下依然有效，使其成为实证应用中更优的选择。在一些温和条件下，我们建立了估计量的渐近正态性，并基于波动率泛函的估计提出了极限方差的一致估计量。我们进行了广泛的模拟研究以验证理论结果。结果表明，我们的估计量相比现有方法具有相对更好的性能，尤其是在跳跃具有无限变差的情况下。此外，我们将所提出的估计量应用于真实的高频数据集，揭示了市场中存在非零的杠杆效应与波动率波动率。