The Distribution of Uncertainty: Evidence from the VIX Options Market

• Author: Clemens Völkert
• DOI: http://doi.org/10.1002/fut.21673
• Date: 01 July 2015
• Published date: 01 July 2015

THE DISTRIBUTION OF UNCERTAINTY:EVIDENCE

FROM THE VIX OPTIONS MARKET

CLEMENS V¨

OLKERT∗

This article investigates the informational content implied in the risk-neutral distribution of

the VIX, a leading barometer of economic uncertainty.We extract the risk-neutral distribution

from VIX option prices over the sample period from 2006 to 2011 using a non-parametric

approach. We analyze the time-series behavior of the option-implied moments and assess

whether the information implied in the risk-neutral distribution has predictive power. The

risk-neutral distribution considerably changed shape during the financial crisis. Furthermore,

risk-neutral moments contain useful information with respect to the likelihood of upward

jumps in volatility.Consistent with investors disliking high levels of economic uncertainty, we

find that the overall shape of the estimated volatility pricing kernel is increasing. For certain

periods, there is a puzzling U-shape. The behavior of the volatility pricing kernel over time

reveals that the financial crisis has affected investors’ attitudes towards risk. ©2014 Wiley

Periodicals, Inc. Jrl Fut Mark 35:597–624, 2015

1. INTRODUCTION

Derivative prices contain information about market participants’ views of future states of

the world. The option-implied information is useful in order to understand current market

conditions and potentially to forecast future market developments. In conjunction with the

objective distribution, the option-implied distribution offers insights into investors’ attitudes

towards risk. In this article, we extract the distribution of volatility using VIX options. We

analyze the behavior of the risk-neutral distribution over time, evaluate its predictive power,

and investigate the stability and monotonicity of the volatility pricing kernel.

Starting in 1993, the Chicago Board Options Exchange (CBOE) published its VIX

index. It expresses the market expectations of the 30-day volatility implied in equity index

options. Since 2003, the CBOE calculates the VIX with a model-free calculation method

that uses the information over the entire strike price range of S&P 500 index (SPX) options.1

Before exchange traded volatility derivatives were introduced, over-the-counter variance and

Clemens V¨

olkert is at the Finance Center M ¨

unster, Westf¨

alische Wilhelms-Universit¨

at M ¨

unster, M ¨

unster,

Germany. He gratefully acknowledges the comments and suggestions from Bob Webb (editor), two anony-

mous referees, Nicole Branger, Patrick Konermann, Alexander Kraftschik, Christoph Meinerding, Olga Se-

dova, Michael Semenischev, and Julian Thimme.

JEL Classification: G12, G13

Correspondence author,Finance Center M ¨

unster, Westf¨

alische Wilhelms-Universit¨

at M¨

unster, Univer-

sit¨

atsstraße 14–16, 48143 M¨

unster, Germany. Tel: +49-251-83-22829, Fax: +49-251-83-22882, e-mail:

clemens.voelkert@gmail.com.

Received October 2012; Accepted February 2014

1The “old” VIX (now VXO) was based on S&P 100 index at-the-money put and call prices and calculated using

the Black and Scholes (1973) option pricing model. For a detailed description of the “new” VIX see Jiang and Tian

(2007), CBOE (2009), and Whaley (2009).

The Journal of Futures Markets, Vol. 35, No.7, 597–624 (2015)

©2014 Wiley Periodicals, Inc.

Published online 15 May 2014 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21673

598 V¨

olkert

volatility swaps were the most direct way to trade volatility. VIX futures were listed at the

CBOE Futures Exchange (CFE) in 2004, VIX options started trading at the CBOE 2 years

later.2

Options on the VIX are particularly suited to study market disruptions. When stock

prices decline the VIX usually increases dramatically.Due to this inverse relationship between

stock prices and volatility, investors consider the VIX as a leading barometer of uncertainty

in the market and commonly call it “investor fear gauge.”3Bloom (2009) points out that

stock market volatility is linked to productivity and demand uncertainty. In this sense, using

VIX options it is possible to extract the distribution of economic uncertainty. The volume

and open interest of VIX derivatives have increased rapidly since their introduction. By now,

VIX options are the second most actively traded contract at the CBOE. The high liquidity

ensures reliable options data to construct risk-neutral distributions.

The papers closest to ours from a methodological point of view are Bliss and Panigirt-

zoglou (2002, 2004) and Kostakis, Panigirtzoglou, and Skiadopoulos (2011). We construct

constant maturity risk-neutral densities using a non-parametric method. A smooth implied

volatility surface is obtained by first interpolating implied volatilities across options with a

given time to expiration and then in the maturity dimension. Afterwards, the result in Breeden

and Litzenberger (1978) is used to extract the risk-neutral density. The papers above apply

this method to equity index options, while we focus on volatility options. To the best of our

knowledge, this is the first study which extracts the risk-neutral distribution from VIX option

prices and analyzes its behavior over time.

There is a large body of literature about the informational content of option-implied

densities from equity indices, interest rates, and exchange rates. Many of these studies fo-

cus on the second moment of the option-implied distribution. Canina and Figlewski (1993),

Christensen and Prabhala (1998), and Jiang and Tian (2005) use the implied volatility to

forecast the future realized volatility of the underlying asset. There is strong empirical ev-

idence that implied volatilities have predictive power and are superior to time-series based

volatility forecasts. Other studies focus on the shape of the risk-neutral distribution around

specific events, like elections and market crashes, and assess whether these events are pre-

dictable or not. Examples include Gemmill (1996), Melick and Thomas (1997), and Coutant,

Jondeau, and Rockinger (2001). Bates (1991) investigates S&P 500 futures options over the

period from 1985 to 1987 and shows that the 1987 stock market crash was anticipated by

the options market. Subsequent research has found inconclusive evidence concerning the

predictability of market crashes using risk-neutral distributions.4

There are several studies which analyze the financial crisis based on stock market volatil-

ity and equity index option prices. Schwert (2011) investigates stock market volatility during

the recent crisis and compares it with previous periods of high volatility. He points out that

compared to the Great Depression the recent crisis was relatively short-lived. Birru and

Figlewski (2012) analyze the events surrounding the collapse of Lehman Brothers using real

time SPX options data. Remarkably, the risk-neutral skewness and kurtosis did decrease in

magnitude. This indicates that drops in the S&P 500 index were not perceived to be more

likely.5Incontrast to these studies, we analyze the risk-neutral volatility distribution. We find

2The increasing popularity of volatility related derivatives has spurred the search for accurate modeling and pricing

tools, see, for example, Sepp (2008a, 2008b), Lin and Chang (2009, 2010), Wang and Daigler (2011), Menc´

ıa and

Sentana (2013), and Branger, Kraftschik, and V¨

olkert (2013).

3See Whaley (2000) and Low (2004). Other option-implied measures of “fear” are discussed in Bollerslev and

Todorov (2011) and Schneider (2012).

4A review of the literature is given by Christoffersen, Jacobs, and Chang (2013).

5Neumann and Skiadopoulos (2013) find that the implied skewness and kurtosis did not change significantly during

the financial crisis.