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Inference in Lévy-type stochastic volatility models

Part of: Inference from stochastic processes Limit theorems Markov processes

Published online by Cambridge University Press:  01 July 2016

Jeannette H. C. Woerner
Jeannette H. C. Woerner*
Affiliation:
University of Göttingen
*
∗ Postal address: Institut für Mathematische Stochastik, University of Göttingen, Maschmühlenweg 8-10, D-37073 Göttingen, Germany. Email address: woerner@math.uni-goettingen.de
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Abstract

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Based on the concept of multipower variation we establish a class of easily computable and robust estimators for the integrated volatility, especially including the squared integrated volatility, in Lévy-type stochastic volatility models. We derive consistency and feasible distributional results for the estimators. Furthermore, we discuss the applications to time-changed CGMY, normal inverse Gaussian, and hyperbolic models with and without leverage, where the time-changes are based on integrated Cox-Ingersoll-Ross or Ornstein-Uhlenbeck-type processes. We deduce which type of market microstructure does not affect the estimates.

Keywords

Stochastic volatility modelLévy processstatistical inferencepower variationintegrated volatilityhigh-frequency data

MSC classification

Primary: 60J75: Jump processes 60F05: Central limit and other weak theorems 62M05: Markov processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 2 , June 2007 , pp. 531 - 549
Copyright
Copyright © Applied Probability Trust 2007 

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