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Forecasting accuracy of stochastic volatility, GARCHand EWMA models under different volatility scenariosJie Ding a & Nigel Meade aa Imperial College London, Tanaka Business School, South Kensington , London SW7 2AZ, UKPublished online: 17 May 2010.
To cite this article: Jie Ding & Nigel Meade (2010) Forecasting accuracy of stochastic volatility, GARCH and EWMA modelsunder different volatility scenarios, Applied Financial Economics, 20:10, 771-783, DOI: 10.1080/09603101003636188
To link to this article: http://dx.doi.org/10.1080/09603101003636188
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Applied Financial Economics, 2010, 20, 771783
Forecasting accuracy of stochastic
volatility, GARCH and EWMA
models under different volatility
Jie Ding and Nigel Meade*
Imperial College London, Tanaka Business School, South Kensington,
London SW7 2AZ, UK
The forecasting of the volatility of asset returns is a prerequisite for many
risk management tasks in finance. The objective here is to identify the
volatility scenarios that favour either Generalized Autoregressive
Conditional Heteroscedasticity (GARCH) or Stochastic Volatility (SV)
models. Scenarios are defined by the persistence of volatility (its robustness
to shocks) and the volatility of volatility. A simulation experiment
generates return series using both volatility models for a range of volatility
scenarios representative of that observed in real assets. Forecasts are
generated from SV, GARCH and Exponentially Weighted Moving
Average (EWMA) volatility models. SV model forecasts are only
noticeably more accurate than GARCH in scenarios with very high
volatility of volatility and a stochastic volatility generating process. For
scenarios with medium volatility of volatility, there is little penalty for
using EWMA regardless of the volatility generating process. A set of
return time series selected from FX rates, equity indices, equities and
commodities is used to validate the simulation-based results. Broadly
speaking, the real series come from the medium volatility of volatility
scenarios where EWMA forecasts are reliably accurate. The robust
structure of EWMA appears to contribute to its greater forecasting
accuracy than more flexible GARCH model.
The forecasting of the volatility of asset returns is
required for many risk management tasks in finance.
The use of Value-at-Risk (VaR) is ubiquitous in
financial institutions and is increasingly widespreadas a risk management tool in corporate institutions.
Future volatility is the crucial input to VaR calcula-
tions; an overestimate of volatility leads to an
opportunity loss due to capital being tied up unne-
cessarily and an underestimate of volatility leads to
risks being under protected. Risk control strategies,
such as delta hedging, are reliant on the estimates offuture volatility for the creation of riskless portfoliosof options and the underlying asset. Mean-variance
portfolio selection relies on the estimates of futurevolatility. Poon and Granger (2003) review the
extensive literature on forecasting the volatility offinancial markets.
Our contribution to this literature is to explorethe comparative effectiveness of the main two
volatility modelling methodologies, Generalized
*Corresponding author. E-mail: email@example.com
Applied Financial Economics ISSN 09603107 print/ISSN 14664305 online 2010 Taylor & Francis 771http://www.informaworld.com
Autoregressive Conditional Heteroscedasticity(GARCH) and Stochastic Volatility (SV) in thecontext of possible volatility scenarios. We use twodimensions, the persistence of volatility (its robust-ness to shocks) and the volatility of volatility, todefine the space of volatility scenarios. We investigateif there are regions where either modelling approachis dominant using the accuracy of volatility forecastsas our measure of dominance. The investigation is intwo parts. First, a simulation experiment is per-formed where data from known volatility models aregenerated to cover the space of volatility scenariosand the accuracy of forecasts prepared from thecompeting models is compared. Second, data fromdifferent financial markets are located within thespace of volatility scenarios and a similar comparisonof forecasting accuracy is carried out.
In addition to forecasts using SV and GARCHmodels, we compute forecasts using ExponentiallyWeighted Moving Average (EWMA) volatility, thespecial case of the GARCH model favoured byRiskMetrics. For the simulated data, we contrast theaccuracy of volatility estimates in-sample and out-of-sample using a range of error measures. Weconclude from this experiment that, for most scenariosand regardless of the data generating process, usinga GARCH volatility forecast involves little penaltycompared to using a SV forecast. SV model forecastsare only noticeably more accurate than GARCH inscenarios with very high volatility of volatility and astochastic volatility generating process. For scenarioswith medium volatility of volatility, there is littlepenalty for using EWMA regardless of the volatilitygenerating process.
In order to validate these simulation-based results,a set of return time series selected from a ForeignExchange (FX) rates, equity indices, equities andcommodities is used. The real series are related to thepersistence and volatility of volatility scenarios andout-of-sample forecasts are generated from the threemethods discussed. We find that, broadly speaking,the real assets come from the medium volatility ofvolatility scenarios where EWMA forecasts are reli-ably accurate.
This article is structured as follows. In Section II,we discuss volatility models and we describe thesimulation experiment in Section III. The validationof our findings using real data is given in Section IVand we give our conclusions in Section V.
II. Volatility Models
A stylized fact of time series of returns on financialassets is the clustering behaviour of volatility.
Two modelling approaches have been used to capture
this behaviour. The GARCH model represents con-
ditional variance as a function of lagged squared
residuals and lagged conditional variance. The sto-
chastic variance model (as implied by its name)
assumes that the variance follows a stochastic pro-
cess. Both approaches will be described below. Note
that we will focus on the basic formulation of each
model, we wish to facilitate comparisons between the
modelling approaches rather than be distracted by the
differences of models within each approach. Our
notation is rt, which is the log-return in period t, this the estimated volatility in period t h, given dataup to period t.
Generalised autoregressive conditionalheteroscedasticity models
The GARCH model was proposed by Bollerslev
(1986), generalizing Engles (1982) Autoregressive
Conditional Heteroscedasticity (ARCH) model. For
surveys of the extensive literature on these models, see
Bollerslev et al. (1992, 1994), and Li et al. (2002). The
GARCH( p, q) model is defined as follows:
rt "t 1
where "t ztt and E(zt) 0 and V(zt) 1. Thevariance, 2t , obeys this process
such that !4 0, i 0, j 0,P
j 5 1.Although there is no consensus about the ideal
GARCH specification (see, e.g. Brailsford and Faff,
1996), there is little doub