Estimation of Tempered Stable Lévy Models of Infinite Variation

Truncated realized quadratic variations (TRQV) are among the most widely used high-frequency-based nonparametric methods to estimate volatility of a process in presence jumps. Nevertheless, truncation level is known critically affect its performance, especially infinite variation In this paper, we study optimal level, mean-square error sense, for semiparametric tempered stable Lévy model. We obtain novel closed-form 2nd-order approximation threshold high-frequency setting. As an application, propose new estimation method, which combines iteratively approximate method moment estimator and TRQVs with newly found small-time threshold. The tested via simulations Blumenthal-Getoor index generalized CGMY model and, localization technique, integrated Heston type Our outperform other alternatives proposed literature when working (i.e., constant), or jump intensity Y larger than 3/2 stochastic volatility.