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Statistics and Its Interface
Volume 15 (2022)
Number 1
Rate-efficient asymptotic normality for the Fourier estimator of the leverage process
Pages: 73 – 89
DOI: https://dx.doi.org/10.4310/21-SII676
Authors
Abstract
We prove a Central Limit Theorem for two estimators of the leverage process based on the Fourier method of Malliavin and Mancino [26], showing that they reach the optimal rate $1/4$ and a smaller variance compared to different estimators based on a pre-estimation of the instantaneous volatility. The obtained limiting distributions of the estimators are supported by simulation results. Further, we exploit the availability of efficient leverage estimates to show, using S&P500 prices, that adding an extra term which accounts for the leverage effect to the Heterogeneous Auto-Regressive volatility model by Corsi [13] increases the explanatory power of the latter.
Keywords
stochastic volatility model, leverage effect, Fourier analysis
2010 Mathematics Subject Classification
42A38, 62F12, 62G05
Received 24 August 2020
Accepted 6 April 2021
Published 11 August 2021