Title: On the Realized Joint Laplace Transform of Volatilities with Application to Test the Volatility Dependence Show Chinese title

Title: 关于波动率的实现联合拉普拉斯变换及其在检验波动率依赖性中的应用

Abstract: In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed estimator is robust to the presence of finite variation jumps in price processes. The related functional central limit theorem for the proposed estimator has been established. Compared with the estimator with non-overlapped increments, the estimator with overlapped increments improves the asymptotic estimation efficiency. Moreover, we study the asymptotic theory of estimator under a long-span setting and employ it to create a feasible test for the dependence between volatilities. Finally, simulation and empirical studies demonstrate the performance of proposed estimators. Show Chinese abstract

Abstract: 在本文中，我们首先研究了在固定时间区间 [0, T] 内，利用高频数据的重叠增量对两个半鞅波动率的经验联合拉普拉斯变换进行估计。所提出的估计量对价格过程中的有限变差跳跃具有鲁棒性。已建立了所提出估计量的相关功能中心极限定理。与使用非重叠增量的估计量相比，使用重叠增量的估计量提高了渐近估计效率。此外，我们在长跨度设定下研究了估计量的渐近理论，并将其用于创建一种可行的检验方法来检验波动率之间的依赖关系。最后，模拟和实证研究展示了所提出估计量的性能。