Volatility forecasts using stochastic volatility models with nonlinear leverage effects

• Author: Kenichiro McAlinn,Teruo Nakatsuma,Asahi Ushio
• DOI: http://doi.org/10.1002/for.2618
• Published date: 01 March 2020
• Date: 01 March 2020

Received: 7 June 2018 Revised: 18 February 2019 Accepted: 6 May 2019

DOI: 10.1002/for.2618

RESEARCH ARTICLE

Volatility forecasts using stochastic volatility models with

nonlinear leverage effects

Kenichiro McAlinn1Asahi Ushio2Teruo Nakatsuma3

1Fox School of Business, Temple

University

2Cogent Labs

3Faculty of Economics, Keio University

Correspondence

Kenichiro McAlinn, Fox School of

Business, Temple University.

Email: kenichiro.mcalinn@temple.edu

Abstract

The leverage effect—the correlation between an asset's return and its

volatility—has played a key role in forecasting and understanding volatility

and risk. While it is a long standing consensus that leverage effects exist and

improve forecasts, empirical evidence puzzlingly does not show that this effect

exists for many individual stocks, mischaracterizing risk, and therefore lead-

ing to poor predictive performance. We examine this puzzle, with the goal to

improve density forecasts, by relaxing the assumption of linearity of the lever-

age effect. Nonlinear generalizations of the leverage effect are proposed within

the Bayesian stochastic volatility framework in order tocapture flexible leverage

structures. Efficient Bayesian sequential computation is developed and imple-

mented to estimate this effect in a practical, on-line manner. Examining 615

stocks that comprise the S&P500 and Nikkei 225, we find that our proposed

nonlinear leverage effect model improves predictive performances for 89% of all

stocks compared to the conventional stochastic volatility model.

KEYWORDS

Bayesian analysis, leverage effect, particle learning, stochastic volatility, volatility forecasting

1INTRODUCTION

The estimation, inference, and prediction of volatility is

one of the most crucial aspects in analyzing data with vari-

ability. In the field of finance and economics, volatility of

financial assets has been investigated with greatscrutiny to

further the understanding of the mechanics and structure

of price movement. One aspect of volatility that has gath-

ered special interest is the correlation between an asset's

return and its volatility; coined the leverage effect.Itisoften

claimed that this correlation is negative, implying that a

negative (positive) shock to an asset's return results in an

increase (decrease) in its volatility.

This phenomenon is intuitive, as we can expect—and

often observe—that an asset under distress exhibits more

variability and uncertainty compared to an asset that is

stable or increasing in price. The term leverage refers to

an economic interpretation given by Black (1976) and

Christie (1982). They state that, when an asset's price

declines, the company's relative debt increases, making

the balance sheet leveraged, resulting in that company

being riskier and therefore its market value more volatile

(see Bekaert and Wu (2000), for example, for different

interpretations and comparisons of the leverage effect).

Though only a hypothesis, this explanation has held

weight in the field and the effect is widely believed to

exist, with supporting evidence from examining major

stock indices ((Nelson, 1991; Glosten et al., 1993; Dumas

et al., 1998), for ARCH-type models and (Jacquier et al.,

1994; Harvey & Shephard, 1996; West & Harrison, 1997;

Jacquier et al., 2004; Yu, 2005; Omori et al., 2007; Naka-

jima & Omori, 2009; Asai & McAleer, 2011; Asai et al.,

2012; Nakajima & Omori, 2012; Takahashiet al., 2013; Shi-

rota et al., 2014), for SV-type models). However,contrary to

Journal of Forecasting. 2020;39:143–154. wileyonlinelibrary.com/journal/for © 2019 John Wiley & Sons, Ltd. 143