Open Access
February 2007 Volatility estimators for discretely sampled Lévy processes
Yacine Aït-Sahalia, Jean Jacod
Ann. Statist. 35(1): 355-392 (February 2007). DOI: 10.1214/009053606000001190


This paper studies the estimation of the volatility parameter in a model where the driving process is a Brownian motion or a more general symmetric stable process that is perturbed by another Lévy process. We distinguish between a parametric case, where the law of the perturbing process is known, and a semiparametric case, where it is not. In the parametric case, we construct estimators which are asymptotically efficient. In the semiparametric case, we can obtain asymptotically efficient estimators by sampling at a sufficiently high frequency, and these estimators are efficient uniformly in the law of the perturbing process.


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Yacine Aït-Sahalia. Jean Jacod. "Volatility estimators for discretely sampled Lévy processes." Ann. Statist. 35 (1) 355 - 392, February 2007.


Published: February 2007
First available in Project Euclid: 6 June 2007

zbMATH: 1114.62109
MathSciNet: MR2332279
Digital Object Identifier: 10.1214/009053606000001190

Primary: 62F12 , 62M05
Secondary: 60H10 , 60J60

Keywords: discrete sampling , efficiency , inference , jumps

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 1 • February 2007
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