Asymmetric Stochastic Volatility Models: Properties and ABC Filter-based Maximum Likelihood Estimation

56 Pages Posted: 3 Jan 2015 Last revised: 15 Dec 2016

See all articles by Xiuping Mao

Xiuping Mao

Zhongnan University of Economics and Law - School of Finance

Veronika Czellar

SKEMA Business School

Esther Ruiz

Charles III University of Madrid - Department of Statistics and Econometrics

Helena Veiga

Charles III University of Madrid - Department of Statistics and Econometrics

Date Written: December 13, 2016

Abstract

In this paper, we derive the statistical properties of a general family of Stochastic Volatility (SV) models with leverage effect which capture the dynamic evolution of asymmetric volatility in financial returns. We provide analytical expressions of moments and autocorrelations of power-transformed absolute returns. Moreover, we use an Approximate Bayesian Computation (ABC) filter-based Maximum Likelihood (ML) method to estimate the parameters of the SV models. In Monte Carlo simulations we show that the ABC filter-based ML accurately estimates the parameters of a very general specification of the log-volatility with standardized returns following the Generalized Error Distribution (GED). The results are illustrated by analyzing series of daily S&P 500 and MSCI World returns.

Keywords: ABC filtering, Leverage effect, SV models, Value-at-Risk

JEL Classification: C11, C51, C58

Suggested Citation

Mao, Xiuping and Czellar, Veronika and Ruiz, Esther and Veiga, Helena, Asymmetric Stochastic Volatility Models: Properties and ABC Filter-based Maximum Likelihood Estimation (December 13, 2016). Available at SSRN: https://ssrn.com/abstract=2544473 or http://dx.doi.org/10.2139/ssrn.2544473

Xiuping Mao

Zhongnan University of Economics and Law - School of Finance ( email )

WenQuan Building, 182# Nanhu Avenue
East Lake High-tech Development Zone
Wuhan, Hubei 430073
China

Veronika Czellar (Contact Author)

SKEMA Business School ( email )

5 quai Marcel Dassault
Suresnes, 92156
France

Esther Ruiz

Charles III University of Madrid - Department of Statistics and Econometrics ( email )

c/ Madrid 126
Getafe (Madrid), 28903
Spain

Helena Veiga

Charles III University of Madrid - Department of Statistics and Econometrics ( email )

c/ Madrid 126
Getafe (Madrid), 28903
Spain

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