具有无穷活动和随机波动率的二维资产价格过程的扩散协变和协跳
Diffusion covariation and co-jumps in bidimensional asset price processes with stochastic volatility and infinite activity Levy jumps
摘要：
在本文中，我们考虑两个过程驱动的扩散和跳跃。跳分量是Levy过程，它们既可以有有限活动，也可以有无限活动.给定离散观测值，我们估计两个扩散部分和联合跳跃之间的协变。联合跳跃的检测允许洞察跳跃分量的依赖结构，并在金融中具有重要的应用。我们的估计是基于阈值原则，允许隔离的跳跃。这项工作遵循Gobbi和Mancini（2006），其中当跳跃分量具有有限活动时，获得了协变估计量的渐近正态性，收敛速度由h的平方根给出。在这里，我们表明，只有当跳跃组件的活动是中等的速度是h的平方根。
英文摘要：
In this paper we consider two processes driven by diffusions and jumps. The jump components are Levy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the two diffusion parts and the co-jumps. The detection of the co-jumps allows to gain insight in the dependence structure of the jump components and has important applications in finance. Our estimators are based on a threshold principle allowing to isolate the jumps. This work follows Gobbi and Mancini (2006) where the asymptotic normality for the estimator of the covariation, with convergence speed given by the squared root of h, was obtained when the jump components have finite activity. Here we show that the speed is the squared root of h only when the activity of the jump components is moderate.
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