An International Comparison of Implied, Realized, and GARCH Volatility Forecasts

• Author: Lazaros Symeonidis,Raphael N. Markellos,Apostolos Kourtis
• Date: 01 December 2016
• Published date: 01 December 2016
• DOI: http://doi.org/10.1002/fut.21792

An International Comparison of Implied,

Realized, and GARCH Volatility Forecasts

Apostolos Kourtis, Raphael N. Markellos,* and Lazaros Symeonidis

We compare the predictive ability and economic value of implied, realized, and GARCH

volatility models for 13 equity indices from 10 countries. Model ranking is similar across

countries, but varies with the forecast horizon. At the daily horizon, the Heterogeneous

Autoregressive model offers the most accurate predictions, whereas an implied volatility model

that corrects for the volatility risk premium is superior at the monthly horizon. Widely used

GARCH models have inferior performance in almost all cases considered. All methods perform

significantly worse over the 2008–09 crisis period. Finally, implied volatility offers significant

improvements against historical methods for international portfolio diversification. © 2016

Wiley Periodicals, Inc. Jrl Fut Mark 36:1164–1193, 2016

1. INTRODUCTION

Volatility is a key concept in finance especially in portfolio selection, option pricing, and risk

management. Despite a variety of shortcomings and alternatives, volatility still lies at the

heart of modern finance. It is not surprising that a vast methodological and empirical

literature exists around the development, assessment, and application of volatility forecasts.

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Unfortunately, it is difficult to draw clear conclusions from the existing literature as research

designs vary considerably across different studies in terms of countries, asset classes, time

periods, forecasting techniques, forecast horizons, and forecast evaluation methods. Our

study aims to overcome this difficulty by comparing some of the most popular volatility

models within a common framework. Our analysis employs 13 equity indices from 10

countries, three forecast horizons, and different market conditions, that is, before, during,

and after the 2008–09 crisis. Comparisons between models are performed on the basis of

different statistical tests and loss functions. Most importantly, we assess the economic

Apostolos Kourtis, Raphael N. Markellos, and Lazaros Symeonidis are at the Norwich Business School,

University of East Anglia, Norwich, UK. We would like to thank two anonymous referees, the editor Robert

Webb, Marcel Prokopczuk, Chardin Wese Simen, and the participants at the 9th International Conference

on Computational and Financial Econometrics for useful comments and suggestions. Part of this project was

completed when Symeonidis was a postgraduate researcher at the ICMA Centre, University of Reading.

JEL Classification: G01, G11, G15, G17

*Correspondence author, Norwich Business School, University of East Anglia, Norwich NR4 7TJ, UK. Tel: þ44 (0)

1603597395, Fax: þ44 (0)1603593343, e-mail: r.markellos@uea.ac.uk

Received March 2015; Accepted March 2016

1

Characteristically, on November 24, 2015, 6,110 papers in Google Scholar and 1,548 research outputs in Scopus

include the term “volatility forecasting.”

The Journal of Futures Markets, Vol. 36, No. 12, 1164–1193 (2016)

© 2016 Wiley Periodicals, Inc.

Published online 20 May 2016 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21792

significance of the competing volatility forecasting models within an international portfolio

choice framework.

The models we consider span the three most prominent families of volatility forecasting

methods. First, we have the GJR-GARCH of Glosten, Jagannathan, and Runkle (1993)

which descends from the ARCH family of historical volatility models. We select this model on

the basis of its popularity among academics and practitioners and the fact that it is often

found to have superior performance against alternative ARCH specifications (e.g., see

Brownlees, Engle, & Kelly, 2012). Second, we use two model specifications based on raw and

volatility risk-premium-adjusted implied volatility levels, respectively. For the adjustment, we

use the technique of DeMiguel, Plyakha, Uppal, and Vilkov (2013) and Prokopczuk and

Wese Simen (2014) which reduces the bias in the raw implied volatility. It is the first time a

study assesses the importance of adjusting for the volatility risk premium in volatility

forecasting in the context of international equity markets. Third, we employ realized

volatility-based forecasts using plain lagged values and the Heterogeneous Autoregressive

(HAR) model of Corsi (2009). The latter approach is becoming increasingly popular due to its

simplicity and modeling accuracy (e.g., see Busch, Christensen, & Nielsen, 2011; Corsi,

Pirino, & Reno, 2010; Giot & Laurent, 2007; Patton & Sheppard, 2015).

We adopt the standard practice of using the daily realized volatility as a proxy for the

“actual”latent volatility. We then employ a battery of different techniques in order to

compare the volatility models on the basis of various statistical and economic criteria. In

order to accommodate the possibility of different forecasting scenaria and tasks, we use

horizons of 1, 5, and 22 days, respectively. We apply univariate Mincer–Zarnowitz as well as

encompassing regressions to assess the information content of each set of volatility forecasts

in an in-sample setting. Out-of-sample analysis is based on the Diebold–Mariano test of

predictive accuracy. Two statistical loss functions are utilized: the root mean-squared error

and the quasi-likelihood. We perform several robustness checks by considering alternative

models, configurations, and estimation periods along with the effect of volatility spillovers

from the United States.

We find that model rankings remain roughly the same across countries but vary with the

forecast horizon. Although the results for the weekly horizon are mixed, the HAR model is

superior at the daily horizon and the implied volatility model yields the best forecasts at the

monthly horizon. The superiority of the volatility risk premium-adjusted implied volatility

forecasts at the monthly horizon is likely due to the fact that all model-free implied volatility

indices have a fixed forecast horizon of 1 month by construction. Our results also reveal that

volatility risk premium-adjusted implied volatility forecasts outperform raw implied volatility

forecasts in most markets under consideration. This finding highlights the importance of

accounting for the volatility risk premium when forecasting volatility using information from

option prices. In line with the literature, comparing raw implied volatility forecasts to lagged

realized volatility forecasts leads to mixed results (see Andersen, Frederiksen, & Staal, 2007b;

Blair, Poon, & Taylor (2001); Jiang & Tian, 2005; Martens & Zein, 2004; Pong, Shackleton,

Taylor, & Xu, 2004). Finally, we find that the historical GJR-GARCH model underperforms

the realized and implied volatility alternatives in almost all cases (similar results are reported

by Fleming, 1998; Jorion, 1995; Andersen, Bollerslev, Diebold, & Labys, 2003; Covrig &

Low, 2003; Giot, 2003; Andersen, Frederiksen, & Staal, 2007b; and Charoenwong,

Jenwittayaroje, & Low, 2009, among others).

Accurate volatility predictions are particularly important during periods of market

turmoil, such as that of 2008–2009, when risks typically soar (see Schwert, 2011). Given that

our dataset spans the period 2000–2012, we examine whether the performance of our

forecasting methods changes between periods of market calmness and unrest. The ranking of

our models is comparable in the periods before, during, and after the crisis. However, all

International Comparison of Volatility Forecasts 1165