Unbiased truncated quadratic variation for volatility estimation in jump diffusion processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Amorino, Chiara¹  Gloter, Arnaud¹ 

[1] Univ Paris Saclay, Univ Evry, Lab Math & Modelisat Evry, CNRS, F-91037 Evry, France

关键词: Levy-driven SDE;    Integrated variance;    Threshold estimator;    Convergence speed;    High frequency data;   

DOI  :  10.1016/j.spa.2020.04.010

来源: Elsevier

【 摘 要 】

The problem of integrated volatility estimation for an Ito semimartingale is considered under discrete high-frequency observations in short time horizon. We provide an asymptotic expansion for the integrated volatility that gives us, in detail, the contribution deriving from the jump part. The knowledge of such a contribution allows us to build an unbiased version of the truncated quadratic variation, in which the bias is visibly reduced. In earlier results to have the original truncated realized volatility well-performed the condition beta > 1/2(2-alpha) on beta (that is such that (1/n)(beta) is the threshold of the truncated quadratic variation) and on the degree of jump activity alpha was needed (see Mancini, 2011; Jacod, 2008). In this paper we theoretically relax this condition and we show that our unbiased estimator achieves excellent numerical results for any couple (alpha, beta). (C) 2020 Elsevier B.Y. All rights reserved.

【 授权许可】

Free