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.
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Acknowledgements
The authors would like to thank the editor, an associate editor and an anonymous referee for their very extensive and constructive suggestions that helped to improve this paper considerably. Xinwei Feng’s work is supported by National Natural Science Foundation of China (No. 12001317) and QILU Young Scholars Program of Shandong University. Zhi Liu’s work is supported by The Science and Technology Development Fund, Macau SAR (No. 202/2017/A3) and National Natural Science Foundation of China (No. 11971507).
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Feng, X., He, L. & Liu, Z. Large Deviation Principles of Realized Laplace Transform of Volatility. J Theor Probab 35, 186–208 (2022). https://doi.org/10.1007/s10959-020-01055-4
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DOI: https://doi.org/10.1007/s10959-020-01055-4
Keywords
- High-frequency data
- Realized Laplace transform of volatility
- Semi-martingale
- Large deviation
- Moderate deviation