The Good and Bad Volatility: A New Class of Asymmetric Heteroskedastic Models
| Author | Ahmed BenSaïda |
| DOI | http://doi.org/10.1111/obes.12398 |
| Date | 01 April 2021 |
| Published date | 01 April 2021 |
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©2020 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 83, 2 (2021) 0305–9049
doi: 10.1111/obes.12398
The Good and Bad Volatility: A New Class of
Asymmetric Heteroskedastic Models
Ahmed BenSa¨
ida†,‡
†College of Business, Effat University, Jeddah, Saudi Arabia
(e-mail: ahmedbensaida@yahoo.com)
‡HEC Sousse – LaREMFiQ Laboratory, University of Sousse, Sousse, Tunisia
Abstract
This paper introduces a new class of tractable asymmetric heteroskedastic models, the good
and bad volatility (GBV). Asymmetry is recognized in the dynamics of GBV components
that correspond to positive and negative shocks respectively. The GBV model allows both
conditional semivariances to evolveaccording to two separate functional forms with differ-
ent semi-definite distributions. An empirical application to six major index returns showsa
fitting improvement over well-known asymmetric volatility models in the financial litera-
ture. The model further leads to significant improvements in forecasting performance.The
derived nontrivial news impact curves convey the dichotomy that asymmetry in financial
returns has different dynamics for positive and negative shocks.
I. Introduction
Asymmetry usually observed in financial market volatility has been much discussed in
the literature (see Ghysels, Plazzi and Valkanov, 2016, and references therein). This phe-
nomenon can be attributed to either the leverage effect (Black, 1976) or feedback effect
(French, Schwert and Stambaugh, 1987). In both cases, returns and volatility are nega-
tively correlated, yet the causality is different. The leverage effect hypothesis supposes
that current returns affect changes in the future conditional volatility, whereas from the
feedback effect viewpoint, changes in the volatility have an impact on time-varying equity
risk premiums and generate shocks to the returns.
Therefore, developing a volatility model that responds to the stylized facts observed in
financial data becomes an urgent concern to risk hedgers, policy makers, portfolio managers
and financial analysts. Several authors (e.g. Chen and Ghysels, 2011; Bekaert, Engstrom
and Ermolov, 2015) arguethat good news and bad news have different impacts, and knowing
a volatility reaction to the sign of a shock is relevant to the analysisof market dynamics and
the implementation of more effective hedging and trading strategies. Engle and Ng (1993)
introduced the news impact curve to show howinfor mation is asymmetricallyincor porated
JEL Classification numbers: G12, G17, C32, C58.
The good and bad volatility model 541
into volatility estimates, and that predictability should separately embrace good news and
bad news.
Recently, the availability of high-frequency (intraday) data led to the development of
realized volatility estimators that are robust to market microstructure noise (Tse and Dong,
2014).1Moreover, Barndorff-Nielsen, Kinnebrouk and Shephard (2010) decomposed the
realized volatility RV into two separate realized semivariance estimators RS+and RS−to
capture changes due to positive and negative shocks respectively. Some researchers have
lately adopted this approach (Patton and Sheppard, 2015; Segal, Shaliastovich and Yaron,
2015; Barun´ık, Koˇcenda and V`acha, 2016) to shed light on the improvement of volatility
forecasts. However, as argued by Chen and Ghysels (2011), high-frequency transactions
might be still contaminated with microstructure noise and stock returns may still contain a
jump component (Cremers, Halling and Weingaum, 2015). Furthermore, volatility predic-
tion models based on these measures are simple linear regressions involving past realized
volatility that ignore the salient dynamics of financial markets and the generated forecasts
are invariant to the observed asymmetries (Barndorff-Nielsen and Shephard, 2007), which
contradicts the concept of news impact curves (Chen and Ghysels, 2011).Another obstruc-
tion to compute the realized volatility is the limited availability of high-frequency data to
few financial instruments and its expensive cost.Therefore, some researchers f avour mod-
elling the volatility over measuring it with intraday data, by incorporating the good news
and bad news effect (Chen and Ghysels, 2011; Feunou, Jahan-Parvar and T´edongap, 2013;
Bekaert et al., 2015; BenSa¨ıda, 2019).
It is noteworthy that El Babsiri and Zako¨ıan (2001) have introduced the concept of
contemporaneous asymmetry, where past up and down moves have different impacts on
the conditional volatility. They treated the variances of positive and negative shocks as
distinct processes, although not necessarily independent and further employed the quasi-
maximum likelihood method to overcome the problem of selecting different distributions.
Pelagatti (2009) adopted this approach using the half generalized error for both shocks to
allow maximum likelihood estimation; still, the errors are constrained to have the same
distributional form. Recently, Palandri (2015) modified El Babsiri and Zako¨ıan’s (2001)
model to utilize a bivariateEGARCH representation. However, in all these formulations, up
and down moves of the conditional volatility processes have the same functional form, yet
with different coefficients. Moreover, their models generate both volatilities – for positive
and negative shocks – independentlyof the actual sign of the retur n, and hardlyoutperfor m
existing asymmetric volatility models.
This paper develops a new class of asymmetric conditional heteroskedastic volatility
models that separately accounts for good news and bad news. Contrary to existing asym-
metric models, the dynamics of the good volatility part (relative to positive shocks) evolve
completely differently than the bad part (relative to negative shocks), and not just an incre-
ment to the same equation when past returns are negative, that is good volatility and bad
volatility evolve according to two separate functional forms with different distributions
vindicating the dichotomous nature of the asymmetry.
1A simple measure of the realized volatility is the sum of intradaily squared returns. More sophisticated measures,
which are robust to microstructure noise and the jump component from continuous changes in asset prices, are also
based on the squared returns.
©2020 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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