Large Deviation Principles of Realized Laplace Transform of Volatility

Xinwei Feng, Lidan He () and Zhi Liu
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Xinwei Feng: Shandong University
Lidan He: University of Macau
Zhi Liu: Zhuhai-UM Science and Technology Research Institute

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 186-208

Abstract: Abstract Under the scenario of high-frequency data, a consistent estimator of the realized Laplace transform of volatility is proposed by Todorov and Tauchen (Econometrica 80:1105–1127, 2012) and a related central limit theorem has been well established. In this paper, we investigate the asymptotic tail behaviour of the empirical realized Laplace transform of volatility (ERLTV). We establish both a large deviation principle and a moderate deviation principle for the ERLTV. The good rate function for the large deviation principle is well defined in the whole real space, which indicates a limit for the normalized logarithmic tail probability of the ERLTV. Moreover, we also derive the function-level large and moderate deviation principles for ERLTV.

Keywords: High-frequency data; Realized Laplace transform of volatility; Semi-martingale; Large deviation; Moderate deviation; 60F10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01055-4

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