Does Fear Spill Over?

• Published date: 01 August 2014
• DOI: http://doi.org/10.1111/ajfs.12055
• Date: 01 August 2014
• Author: Cathy Yi‐Hsuan Chen

Does Fear Spill Over?

Cathy Yi-Hsuan Chen*

Department of Finance, Chung Hua University

Received 19 November 2013; Accepted 11 March 2014

Abstract

This paper develops a new methodology for analyzing fear spillovers between four implied

volatility indices (MVX in Canada, VXJ in Japan, VDAX in Germany and VIX in the United

States) using a copula-based bivariate Markov-switching model. We consider a parameteriza-

tion of the Markov-switching model that allows for four possible states (consisting of combi-

nations of either low or high expected volatilities). This model also combines selected

copulas to describe the dependence pattern between different markets. The results show that

dependencies, contagions and causalities between the four implied volatility index levels are

strongly supported by the data in all copulas. From the dynamic and asymmetric analysis,

the results indicate that the linkages between implied volatility indices are more pronounced

when the indices rise.

Keywords Copula; Spillover; Implied volatility; Contagion; Markov-switching model

JEL Classification: G1, G15

1. Introduction

As the world market has become more integrated over the past three decades (For-

bes and Rigobon, 2002; Bekaert et al., 2005; Pukthuanthong and Roll, 2009), finan-

cial markets have witnessed several financial crises that originated in one market

and then, simultaneously or after a short period of time, spread to other markets.

1

The transmission of the stock index level and volatility has been widely examined.

Existing studies have considered contemporaneous and lead-lag volatility spillovers

between and among different equity markets. They have dealt with spillovers of

volatility from one market to another, focusing on shocks to volatility in a GARCH

framework. Readers may refer to King and Wadhwani (1990), Ng (2002) and

*Corresponding author: Cathy Yi-Hsuan Chen, Department of Finance, Chung Hua Univer-

sity, No. 707, Sec. 2, WuFu Road, Hsinchu 300, Taiwan. Tel: +886-3-5186057, Fax: +886-3-

5186054, email: cathy1107@gmail.com.

1

During the last two decades, a series of financial and currency crises have occurred, many

carrying regional or even global consequences: the 1987 Wall Street crash, the 1992 European

monetary system collapse, the 1994 Mexican pesos crisis, the 1997 “Asian flu,” the 1998

“Russian cold,” the 1999 Brazilian devaluation, the 2000 Internet bubble burst, the July 2001

default crisis in Argentina, and the 2008–2009 United States subprime crisis.

Asia-Pacific Journal of Financial Studies (2014) 43, 465–491 doi:10.1111/ajfs.12055

©2014 Korean Securities Association 465

Bekaert et al. (2005), among others. Instead of employing the volatility from a

GARCH framework to study the spillover issue, the extant literature has mostly

studied the notion of an expected volatility spillover, which is free of a model error

problem.

2

The purpose of this paper is two-fold. First, we present an original investigation

of the spillover effects of option-implied volatility indices (as a proxy for “fear”)

among four different markets: the United States, Japan, Canada, and Germany.

These option-implied volatility indices provide investors an opportunity to look at

market volatility from a forward-looking perspective.

Whaley (1993) and Fleming et al. (1995) were the pioneers in employing the

implied volatility index as a measure of expected volatility. The CBOE constructs

an implied volatility index, the VIX, from these American-style option prices. Com-

puted from the most actively traded index options market in the world, the VIX

represents option traders’ best guess for risk in the S&P 500. The VIX has also been

nicknamed “the fear gauge” (Whaley, 2000; Low, 2004) or “the sentiment index” by

the Wall Street Journal. For measuring a market’s perception of risk from empirical

data, the VIX is arguably the best option currently available.

Second, we present an alternative way of detecting the spillover effect of

expected volatility from one economy to another, a way that is robust to the struc-

tural breaks of the volatility process.

3

We consider a parameterization of the Mar-

kov-switching model used in Phillips (1991), Ravn and Sola (1995), Edwards and

Susmel (2001), Baele (2005), and Bialkowski and Serwa (2005) that allows for four

possible states of nature (consisting of combinations of either low or high expected

volatilities), and we test whether one country’s volatility spills over to another dur-

ing a period of crisis (defined as periods of high expected volatility). This approach

is useful because it accounts for the fact that a crisis (and its transmission) is bet-

ter characterized as a sporadic event, rather than a structural relationship between

2

Many studies have examined the relationship between risk and return by using volatility

metrics that are statistically estimated from historical data. Statistical estimation generally

produces two types of errors: sampling errors and model misspecification errors. The VIX is

different from these volatility estimates. It is not a statistical estimate but a quantity backed

out from an option-pricing model. Therefore, sampling error is no longer an issue. More-

over, if the model is robust to small variations in specification and is widely used by traders

in setting prices (i.e. the market uses a similar model), then the error due to model misspeci-

fication will be small. The tremendous depth of this index option market ensures that the

transacted prices are representative of the aggregate consensus.

3

Since Diebold (1986) and Lamoreaux and Lastrapes (1990), it has been well known that

misleading inferences on the persistence of the volatility process may be caused by unac-

counted for structural breaks. Moreover, the volatility patterns frequently show evidence of

nonlinearity (Frijns and Schotman, 2006). Econometric models where structural change can

be modeled endogenously have been proposed by Cai (1994) and Hamilton and Susmel

(1994) for the Markov-switching ARCH model.

C. Y.-H. Chen

466 ©2014 Korean Securities Association