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The Annals of Statistics 2007, Vol. 35, No. 1, 355392
 

Summary: The Annals of Statistics
2007, Vol. 35, No. 1, 355ş392
DOI: 10.1214/009053606000001190
ę Institute of Mathematical Statistics, 2007
VOLATILITY ESTIMATORS FOR DISCRETELY SAMPLED
L╔VY PROCESSES
BY YACINE A¤T-SAHALIA1 AND JEAN JACOD
Princeton University and UniversitÚ de Paris-6
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 LÚvy process. We distinguish be-
tween 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 con-
struct estimators which are asymptotically efficient. In the semiparametric
case, we can obtain asymptotically efficient estimators by sampling at a suffi-
ciently high frequency, and these estimators are efficient uniformly in the law
of the perturbing process.
1. Introduction. Models allowing for sample path discontinuities or jumps
are becoming increasingly popular, especially in mathematical finance. Among
jump processes, LÚvy processes play a central role due to their analytical tractabil-

  

Source: A´t-Sahalia, Yacine - Program in Applied and Comptutational Mathematics & Department of Economics, Princeton University

 

Collections: Mathematics