ESTIMATING THE DIFFUSION PART OF THE COVARIATION BETWEEN TWO VOLATILITY MODELS WITH JUMPS OF LÉVY TYPE
ESTIMATING THE DIFFUSION PART OF THE COVARIATION BETWEEN TWO VOLATILITY MODELS WITH JUMPS OF LÉVY TYPE
复制标题
估计具有 LÉVY 型跳跃的两个波动率模型之间协变的扩散部分
DOI：
10.1142/9789812709394_0035
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
C. Mancini
中科院分区：
文献类型：
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作者：
F. Gobbi;C. Mancini
估计扩散协变部分的一种常用方法是取两个过程增量的叉积之和；然而，在存在跳跃分量的情况下，这种估计器可能会有很大的偏差，因为它接近也包含协跳的二次协变。我们的估计器基于阈值原理，允许隔离跳跃。因此，我们找到了一个一致的估计量。在活动跳跃分量有限的情况下，估计器也是渐近高斯的。我们在四个不同的模拟模型上评估了我们对有限样本的估计器的性能。
A commonly used approach to estimate the diffusion covariation part is to take the sum of the cross products of the two processes increments; however this estimator can be highly biased in the presence of jump components, since it approaches the quadratic covariation containing also the co-jumps. Our estimator is based on a threshold principle allowing to isolate the jumps. As a consequence we find an estimator which is consistent. In the case of finite activity jump components the estimator is also asymptotically Gaussian. We assess the performance of our estimator for finite samples on four different simulated models.