无穷变差的回火稳定Lévy模型的估计
Estimation of Tempered Stable Lévy Models of Infinite Variation
摘要：
提出了半参数回火稳定Lévy模型估计的一种新方法。估计过程结合迭代近似半参数矩估计方法，截断实现二次变差（TRQV），和一个新发现的小时间高阶近似的最佳阈值的TRQV的回火稳定过程。该方法是通过模拟测试估计的波动率和Blumenthal-Getoor指数的广义CGMY模型，以及集成的波动率的Heston型模型与CGMY跳跃。该方法优于文献中提出的其他有效的替代方案时，与Lévy过程（即，波动率是恒定的），或者当跳跃强度指数$Y$大于$3/2$时存在随机波动率。
英文摘要：
We propose a new method for the estimation of a semiparametric tempered stable Lévy model. The estimation procedure combines iteratively an approximate semiparametric method of moment estimator, Truncated Realized Quadratic Variations (TRQV), and a newly found small-time high-order approximation for the optimal threshold of the TRQV of tempered stable processes. The method is tested via simulations to estimate the volatility and the Blumenthal-Getoor index of the generalized CGMY model as well as the integrated volatility of a Heston-type model with CGMY jumps. The method outperforms other efficient alternatives proposed in the literature when working with a Lévy process (i.e., the volatility is constant), or when the index of jump intensity $Y$ is larger than $3/2$ in the presence of stochastic volatility.
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