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ESTIMATION OF VOLATILITY FUNCTIONS IN JUMP DIFFUSIONS USING TRUNCATED BIPOWER INCREMENTS

Published online by Cambridge University Press:  08 October 2020

Jihyun Kim ,
Joon Y. Park  and
Bin Wang
Jihyun Kim*
Affiliation:
Toulouse School of Economics University of Toulouse Capitole
Joon Y. Park
Affiliation:
Indiana University Sungkyunkwan University
Bin Wang
Affiliation:
Harbin Institute of Technology, Shenzhen
*
Address correspondence to Jihyun Kim, Toulouse School of Economics, Toulouse 31000, France; e-mail: jihyun.kim@tse-fr.eu.
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Abstract

In this article, we introduce and analyze a new methodology to estimate the volatility functions of jump diffusion models. Our methodology relies on the standard kernel estimation technique using truncated bipower increments. The relevant asymptotics are fully developed, allowing for the time span to increase as well as the sampling interval to decrease, and accommodate both stationary and nonstationary recurrent processes. We evaluate the performance of our estimators by simulation and provide some illustrative empirical analyses.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 5 , October 2021 , pp. 926 - 958
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

We thank the Editor Peter C.B. Phillips, the Co-Editor Dennis Kristensen, and three anonymous referees for many helpful comments. For useful discussions, we are also grateful to Yacine Aït-Sahalia, Yoosoon Chang, Nour Meddahi, Mathieu Rosenbaum, Roberto Renò, Jun Yu, and the participants at 2015 Toulouse Financial Econometrics Conference, 2016 Princeton-QUT-SJTU-SMU Econometrics Conference and 2017 Asian Meeting of Econometric Society. Jihyun Kim is grateful to the French Government and the ANR for support under the Investissements d’Avenir program, grant ANR-17-EURE-0010. Bin Wang gratefully acknowledges financial support provided to him by Shenzhen Key Research Base of Humanities and Social Sciences.

References

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