The information content of option‐implied tail risk on the future returns of the underlying asset

• Date: 01 April 2018
• DOI: http://doi.org/10.1002/fut.21887
• Published date: 01 April 2018
• Author: Yaw‐Huei Wang,Kuang‐Chieh Yen

Received: 7 September 2017

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Accepted: 16 September 2017

DOI: 10.1002/fut.21887

RESEARCH ARTICLE

The information content of option-implied tail risk on the future

returns of the underlying asset

Yaw-Huei Wang

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Kuang-Chieh Yen

Department of Finance, National Taiwan

University, Taipei, Taiwan

Correspondence

Yaw-Huei Wang, Department of Finance,

National Taiwan University, No. 1

Roosevelt Road, Section 4, Taipei 106,

Taiwan.

Email: wangyh@ntu.edu.tw

Funding information

Ministry of Science and Technology of

Taiwan

We compile option-implied tail loss and gain measures based on a deep out-of-the-

money option pricing formula derived by applying “extreme value theory,”and then

use these measures to investigate the information content of option-implied tail risk

on the future returns of the underlying assets. Our empirical analysis shows that both

tail measures implied by S&P 500 and VIX options can predict future changes in the

corresponding underlying assets and are informative on the future returns of the S&P

500 index. The relationships are particularly strong during periods of economic

recession and driven by the tail-risk premium.

KEYWORDS

extreme value theory, options, S&P 500, tail measures, VIX

JEL CLASSIFICATION

G13, G14

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INTRODUCTION

Prices in the derivatives markets are widely recognized as containing forward-looking information, with a number of studies

having empirically investigated whether the information gleaned from the options markets reflects the future price dynamics of

the underlying assets.

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Within the extant related literature, aside from the focus on implied volatility,

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some option-implied

information proxies, such as implied correlations and market variance risk premium, have also been shown to be useful

predictors of market returns.

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However, all of these measures represent the general expectations on the price distribution of the

underlying assets.

In one particular study, Pan and Poteshman (2006) demonstrate that the trading of options with higher leverage tends to be

more informative with regard to the future dynamics of the underlying asset. This provides signals that theinformation relating to

the tail properties of the price distribution of the underlying asset could be useful in determining its future dynamics.

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Prior studies on the prediction of returns with option-implied information include Whaley (2000), Giot (2005), Banerjee, Doran, and Peterson (2007),

Bakshi, Panayotov, and Skoulakis (2011), Feunou, Fontaine, Taamouti, and Tedongap (2014), Andersen et al. (2015) and Bollerslev et al. (2015).

Christoffersen et al. (2013) also provide a comprehensive survey on option-implied information in forecasting.

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The CBOE VIX index is invariably used as the proxy for implied volatility. This is compiled from the market prices of S&P 500 index options as the

means of approximating the expected aggregate volatility of the S&P 500 index during the subsequent 30 calendar-day period. Following Whaley (2000),

in which the VIX is found to be an effective “fear gauge,”Giot (2005) finds a strong negative correlation between the contemporaneous changes, along

with a positive relationship between the current levels of the implied volatility indices and future market index returns. Similar findings are also reported

by Guo and Whitelaw (2006) and Banerjee et al. (2007).

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Detailed explanations of these market return predictors are provided in Bollerslev, Tauchen, and Zhou (2009) and Buss and Vilkov (2012).

J Futures Markets. 2018;38:493–510. wileyonlinelibrary.com/journal/fut © 2017 Wiley Periodicals, Inc.

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Against this backdrop, we set out in this study to explore the way in which option-implied tail information can be extracted, and

whether the information is of use in predicting the price dynamics of the underlying asset. Although the majority of the prior studies

have tended to adopt approaches based upon the central distribution of the underlying asset as the means of extracting option-implied

information, some of the more recent studies have focused their attention on the information implied in the tail of the price distribution.

Du and Kapadia (2012) construct a jump index using the difference between the CBOE VIX and the model-free volatility

proposed by Bakshi, Kapadia, and Madan (2003), which is found to be capable of predicting the future returns of the S&P 500

index. Andersen, Fusari, and Todorov (2015) provide evidence to show that the tail factor is a critical element in the forecasting

of the monthly market returns, as opposed to future volatility or jump risks. Bollerslev et al. (2015) also demonstrate that the left-

tail jump risk premium is capable of predicting monthly market returns.

According to “extreme-value theory”(EVT), the option pricing model is derived from certain distributional approximations

which remain valid regardless of the true distribution of the underlying asset price. Therefore, following the theoretical

framework of Hamidieh (2017),

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we investigate whether the tail risk information extracted from the out-of-the-money (OTM)

options in the S&P 500 index and the VIX can be of use in predicting the dynamics of the corresponding underlying asset.

Given thatnumerous empirical observations haverevealed a negative relationship betweenthe VIX and the S&P 500 index, we

examinewhether the tail risk information impliedin VIX options can also providea predictive function with regard tothe dynamics

of the S&P 500 index, and if so, whether its information content overlaps with that of the information implied in the S&P 500

options. In specific terms, using the EVT-based deep-OTM option-pricing model proposed by Hamidieh (2017), we extend the

methodof Vilkov and Xiao (2013) to calculate the tail lossmeasure (TLM) and tail gain measure (TGM) fromthe option prices, and

then go on to compile the respective measures from the S&P 500 and VIX options for subsequent empirical analysis.

If the tail measures do indeed provide information content on the future returns or levels of the underlying asset, then we

would expect to find a positive predictive relationship for the tail gain measure, as compared to a negative relationship for the tail

loss measure. Alternatively, if the tail measures represent the levels of tail risk, and investors require compensatory premiums for

taking the risk, then we would expect to find a positive predictive relationship for both the tail gain and loss measures. Our main

empirical results reveal the following.

First, both the tail loss and gain measures compiled from S&P 500 index options are found to have positive associations with

the future returns of the S&P 500 index, with this relationship being found to be stronger for the tail loss measure, and the

information content of these tail measures differing from that of the VIX, although the tail measures are found to be highly

correlated with the VIX. Second, both the tail loss and gain measures compiled from VIX options are found to positively predict

the VIX level, with the effect being stronger for the tail gain measure.

Third, the S&P 500 tail loss measure and the VIX tail gain measure are both found to provide significant information on the

future returns of the S&P 500 index, with the effect being stronger for the S&P 500 tail loss measure. Fourth, almost all of the

predictive relationships are found to be particularly robust during periods of economic recession. Finally, we show that all of the

predictive relationships are driven by the tail-risk premiums and that they are generally quite short-lived.

The primary objective of this s tudy is to investigate whether th e option-implied tail measures provide information with

predictive ability on the future retu rns of the underlying asset. Among those stu dies investigating the effects of option-

implied information conten t on the future dynamics of the unde rlying asset, greater focus is currently being placed on the

option-implied tail infor mation.

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We follow the methodology of Ham idieh (2017) and Vikov and Xiao (2013) to select the

Black–Scholes–Merton model (the most po pular and concise framework) a nd then use EVT to obtain a deep-OTM opti on-

pricing equation. This provides us wi th a new channel for the estimation of the tail shape and scale parameters through wh ich

a conditional tail loss or gain ca n be identified (Vilkov & Xiao, 2013 ).

We adopt the Black–Scholes–Merton model essentially because we wish to avoid potential estimation errors due to too many

parameters, and in contrast to the studies undertaken by Andersen et al. (2015) and Bollerslev et al. (2015), rather than monthly

data frequency, the frequency used in the present study is set at the daily level. We also contribute to the extant literature by

extending the research to cover the implied tail measures from VIX options, investigating the joint information content of S&P

500 and VIX option implied tail measures on the future dynamics of the S&P 500 index, and considering the impacts of the

business cycle on the tail risk.

The remainder of this paper is organized as follows. Section 2 provides discussions on extreme value theory and the deep-

OTM option-pricing formula, followed in section 3 by a review of the literature and the development of our testable hypotheses.

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Hamidieh (2017) derives a new option pricing formula based upon extreme-value theory as the means of estimating the tail shape parameter of the risk

neutral density.

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See for example, Du and Kapadia (2012), Andersen et al. (2015), Bollerslev et al. (2015), and Park (2015).

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WANG AND YEN