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

Maria Elvira Mancino (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Italy)

Giacomo Toscano (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Italy)

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