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

Full Text (PDF format)

Received 24 August 2020

Accepted 6 April 2021

Published 11 August 2021