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Journal of Banking & Finance 37 (2013) 3388–3400 Contents lists available at SciVerse ScienceDirect Journal of Banking & Finance journal homepage: The crosssectional relation between conditional heteroskedasticity, the implied volatility smile, and the variance risk premium Louis H. Ederington a,⇑, Wei Guan b a b Finance Division, Michael F. Price College of Business, University of Oklahoma, 205A Adams Hall, Norman, OK 73019, USA College of Business, University of South Florida St. Petersburg, 140 Seventh Avenue South, St. Petersburg, FL 33701, USA a r t i c l e i n f o Article history: Received 11 October 2012 Accepted 14 April 2013 Available online 17 May 2013 JEL classiﬁcation: G13 G10 G12 a b s t r a c t This paper estimates how the shape of the implied volatility smile and the size of the variance risk premium relate to parameters of GARCHtype timeseries models measuring how conditional volatility responds to return shocks. Markets in which return shocks lead to large increases in conditional volatility tend to have larger variance risk premia than markets in which the impact on conditional volatility is slight. Markets in which negative (positive) return shocks lead to larger increases in future volatility than positive (negative) return shocks tend to have downward (upward) sloping implied volatility smiles. Also, differences in how volatility responds to return shocks as measured by GARCHtype models explain much, but not all, of the variations in excess kurtosis and multiperiod skewness across different markets. Ó 2013 Elsevier B.V. All rights reserved. Keywords: Implied volatility Volatility smile Variance risk premium GARCH Conditional heteroskedasticity 1. Introduction Along with jump risk, a leading explanation for both the implied volatility smile and the variance risk premium is stochastic volatility, i.e., the possibility that volatility will change in the future. While changes in volatility could be associated with many factors or occur randomly, one pattern which has been well documented by GARCH model estimations is that in many markets the conditional return variance responds to return shocks. For instance, in most markets, the conditional variance tends to rise following large absolute return shocks and fall following periods of very small price movements. To the extent that ﬂuctuations in the variance of returns are associated with return shocks, as GARCH model estimations indicate, investors ...
The crosssectional relation between conditional heteroskedasticity,
the implied volatility smile, and the variance risk premium
Louis H. Ederington
a,
⇑
, Wei Guan
b
a
Finance Division, Michael F. Price College of Business, University of Oklahoma, 205A Adams Hall, Norman, OK 73019, USA
b
College of Business, University of South Florida St. Petersburg, 140 Seventh Avenue South, St. Petersburg, FL 33701, USA
article info
Article history:
Received 11 October 2012
Accepted 14 April 2013
Available online 17 May 2013
JEL classiﬁcation:
G13
G10
G12
Keywords:
Implied volatility
Volatility smile
Variance risk premium
GARCH
Conditional heteroskedasticity
abstract
This paper estimates how the shape of the implied volatility smile and the size of the variance risk pre
mium relate to parameters of GARCHtype timeseries models measuring how conditional volatility
responds to return shocks. Markets in which return shocks lead to large increases in conditional volatility
tend to have larger variance risk premia than markets in which the impact on conditional volatility is
slight. Markets in which negative (positive) return shocks lead to larger increases in future volatility than
positive (negative) return shocks tend to have downward (upward) sloping implied volatility smiles. Also,
differences in how volatility responds to return shocks as measured by GARCHtype models explain
much, but not all, of the variations in excess kurtosis and multiperiod skewness across different markets.
Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction
Along with jump risk, a leading explanation for both the implied
volatility smile and the variance risk premium is stochastic volatil
ity, i.e., the possibility that volatility will change in the future.
While changes in volatility could be associated with many factors
or occur randomly, one pattern which has been well documented
by GARCH model estimations is that in many markets the condi
tional return variance responds to return shocks. For instance, in
most markets, the conditional variance tends to rise following
large absolute return shocks and fall following periods of very
small price movements. To the extent that ﬂuctuations in the var
iance of returns are associated with return shocks, as GARCH mod
el estimations indicate, investors should anticipate greater future
variance ﬂuctuations in markets in which the variance responds
sharply to return shocks than in markets in which the impact of
the same size shock on the conditional variance is slight. This is
the idea explored in the present paper. In particular, we investigate
how variations in the implied volatility smile and in the variance
risk premium across different markets relate to differences in
how conditional volatility responds to surprise return shocks as
measured by GARCHtype models.
Consider, for instance, the most studied implied volatility smile
– that on options on US equity indices, such as the S&P 500. It is
wellknown that Black–Scholes (BS) implied volatilities on US
stock market index options decline with the strike price in a smirk
pattern. While there are other possible explanations, such as jump
risk, the hedging pressure hypothesis of Bollen and Whaley (2004)
and Ederington and Guan (2002), the Bakshi et al. (2003) skewness
hypothesis, or the transaction cost hypothesis of Peña et al. (1999),
one popular explanation of this smirk pattern is that it arises be
cause volatility is stochastic and tends to be negatively correlated
with recent stock market returns.
1
According to this explanation,
because volatility tends to increase when the market drops, large
multiperiod market declines are more likely than large multiperiod
market increases imparting a negative skewness to multiperiod re
turns and increasing the likelihood that far outofthemoney (OTM)
puts will ﬁnish in the money thereby raising their price and implied
03784266/$  see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jbankﬁn.2013.04.017
⇑
Corresponding author. Tel.: +1 405 325 5591.
Email addresses: lederington@ou.edu (L.H. Ederington), wguan@mail.usf.edu
(W. Guan).
1
For prominent examples, see Heston (1993), Duan (1995), Bakshi et al. (1997),
Bates (2000), Heston and Nandi (2000), Andersen et al. (2002), Christoffersen et al.
(2006) and Christoffersen et al. (2010). See also the smile chapter in Hull (2006).
However, Bates (2000) and Andersen et al. (2002) conclude that volatility changes
alone are insufﬁcient to explain the stock index smile. For a similar correlation
argument for jump risk, see Câmara et al. (2011).
Journal of Banking & Finance 37 (2013) 3388–3400
Contents lists available at SciVerse ScienceDirect
Journal of Banking & Finance
journal homepage: www.elsevier.com/locate/jbf
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