Volatility information implied in the term structure of VIX

• DOI: http://doi.org/10.1002/fut.21964
• Published date: 01 January 2019
• Date: 01 January 2019

Received: 12 October 2016

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Accepted: 5 August 2018

DOI: 10.1002/fut.21964

RESEARCH ARTICLE

Volatility information implied in the term structure

of VIX

Kai‐Jiun Chang

1

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Mao‐Wei Hung

2

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Yaw‐Huei Wang

3

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Kuang‐Chieh Yen

4

1

Taiwan Academy of Banking and

Finance, Taipei, Taiwan

2

Department of International Business,

National Taiwan University, Taipei,

Taiwan

3

Department of Finance, National Taiwan

University, Taipei, Taiwan

4

Department of Economics, Soochow

University, Taipei, Taiwan

Correspondence

Yaw‐Huei Wang, Department of Finance,

National Taiwan University, No. 1,

Section 4, Roosevelt Road, Taipei 106,

Taiwan.

Email: wangyh@ntu.edu.tw

Funding information

National Taiwan University, Grant/

Award Number: R7743; Ministry of

Science and Technology, Taiwan,

Grant/Award Number:

101‐2628‐H‐002‐002‐MY3

Abstract

This study uses multiple maturity‐independent variables to examine whether

the volatility information implied in the term structure of volatility index can

improve the prediction of realized volatility. The empirical results for the S&P

500 index show that, in terms of both the in‐sample estimation and out‐of‐

sample forecasting, the term structure variables provide substantial incremental

contribution to the models with only level variables. Our empirical results are

robust to various forms of volatility, alternative ways to develop the term

structure variable, the impact of macroeconomic variables, and alternative

underlying assets.

KEYWORDS

forecasting, options, term structure, VIX, volatility

JEL CLASSIFICATION

G13, G17

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INTRODUCTION

Although the Chicago Board Options Exchange (CBOE) introduced a new approach to compute the implied volatility index

(VIX) in 2003, it is still maturity dependent. Even though most previous studies adopt the CBOE standard of the 30‐day VIX,

the information on the term structure is still missing. Because volatility, unlike a general asset price, behaves in accordance

to some special stylized facts such as clustering and mean‐reversion, the term structure of the VIX may reflect market

participants’expectation on how volatility will change. Therefore, this study investigates the role of the VIX term structure in

volatility forecasting. In general, the empirical results support the significant incremental contribution of the information on

the VIX term structure for forecasting realized volatility. In particular, the improvement made by the term structure for the

in‐sample and out‐of‐sample prediction can reach 4.77% and 6.02%, respectively.

Asset return volatility plays an important role in assessing derivative prices and managing financial risks. Due to

properties such as persistency and mean‐reversion, volatility is much more predictable than returns.

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In particular,

since Black and Scholes (1973) introduced their option pricing formula, option prices have been a source of valuable

information for volatility forecasting. Poon and Granger (2003) provide a comprehensive survey of volatility forecasting

studies and conclude that, although biased, option‐implied volatility is the best predictor of realized volatility. In

J Futures Markets. 2019;39:56–71.wileyonlinelibrary.com/journal/fut56

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© 2018 Wiley Periodicals, Inc.

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Many studies attribute volatility forecasting inaccuracy to the use of a very noisy proxy for volatility, such as squared daily returns (Andersen & Bollerslev, 1998). When realized volatility is measured

using intraday prices, forecasts of volatility are more accurate (e.g., Blair, Poon, & Taylor, 2001; Li, 2002; Martens & Zein, 2004; Pong, Shackleton, Taylor, & Xu, 2004).

addition, numerous previous studies confirm the superiority of option‐implied volatility in volatility forecasting (Blair

et al., 2001; Ederington & Guan, 2002; Fleming, 1998; Jiang & Tian, 2005; Xu & Taylor, 1995).

Implied volatility usually refers to the volatility value of the Black–Scholes option price and the corresponding

market price. However, the strike price and the expiration of the option contract also affect implied volatility. Thus,

among the many available implied volatilities, which one is most appropriate is an empirical issue. Most early studies

adopt the implied volatility recovered from the nearest‐month at‐the‐money (ATM) contract. In 1993, the CBOE

introduced the VIX, which consists of eight S&P 100 index options that include near at‐the‐money, nearby, and second

nearby calls and puts. This index reflects the implied volatility of a 30‐calendar‐day ATM option. About 10 years later,

the CBOE introduced a revamped VIX computed by a model‐free formula, which is based on the theoretical work of

Britten‐Jones and Neuberger (2000), Carr and Madan (1998), and Demeterfi, Derman, Kamal, and Zou (1999), rather

than the Black–Scholes formula. Rather than using eight near‐ATM prices, the updated VIX uses S&P 500 index options

with a wide range of strike prices. As expected, the updated VIX contains more information than the previous version

and thus provides improved volatility forecasting (Jiang & Tian, 2005).

Nonetheless, although the model‐free implied volatility index incorporates a volatility smile, it is still maturity

dependent. The VIX is usually regarded as a 30‐day implied volatility index, even though it interpolates two nearby

model‐free implied volatilities. Therefore, studies that use the new formula to investigate the predictive power of

implied volatility must choose a particular maturity. Almost all studies in this fast‐growing stream of literature on

implied volatility only consider the 30‐day maturity.

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Thus, most prior research that uses the VIX to investigate

volatility forecasting does not include information on the volatility term structure. Because volatility exhibits some

unique properties such as clustering and mean‐reversion, its term structure should contain market participants’

expectation of the change of volatility. Thus, we explore whether this information can be extracted from the VIX term

structure, and, if so, whether it can improve the performance of the VIX in volatility forecasting.

Following Wang and Yen (2018), we use three approaches to extract the information implied in the VIX term

structure. First, we adopt a two‐factor model to transform the maturity‐dependent squared VIX into maturity‐

independent level and term structure variables. In addition, we generate two sets of level and term structure variables

using principal component analysis (PCA) and two squared VIX levels with different maturities. We empirically

examine the performance of the models with and without the term structure variables on volatility forecasting of the

S&P 500 index returns and find that both the in‐sample and out‐of‐sample results support the significant incremental

contribution of the term structure variables to the models with the level variables only. The level variables extracted

from the term structure of squared VIX share the information content of the commonly adopted 30‐day VIX, which the

literature widely finds to be the most powerful predictor for realized volatility. Therefore, the term structure variables

possess additional effective information for the determination of future realized volatility, given that the term structure

variable generated by PCA explains little variation of the term structure of squared VIX.

To strengthen the robustness of our empirical results, we conduct an in‐sample analysis using various forms of

volatility (i.e., standard deviation and logarithmic standard deviation), alternative methods of developing the term

structure variable (i.e., different pairs of maturities of VIX), multiple ways of measuring the impact of the

macroeconomic variables (i.e., the variance of industrial production, monetary base, and producer price index returns),

and an alternative underlying asset (the NASDAQ 100 index). For the NASDAQ 100 index, we also conduct an out‐of‐

sample analysis. The conclusions drawn from our empirical results remain unaltered.

The remainder of the paper is organized as follows. Section 2 gives a brief description of our data and filtration rules.

Sections 3 and 4 introduce the approaches to extract information from the VIX term structure and the empirical models,

respectively. Section 5 provides the empirical results and discusses their implications for both in‐sample and out‐of‐

sample forecasting. We conduct several robustness tests in Section 6 and offer our conclusions in Section 7.

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DATA

The primary data set consists of the daily best bid and ask prices of the S&P 500 index options, which come from

OptionMetrics, along with the details of the contracts including type (call or put), time‐to‐maturity, and strike price. We

use the mid‐quotes (averages of bid and ask prices) to represent the market prices. From the same database, we obtain

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Numerous studies investigate the implied volatility smile. See, for example, Rubinstein (1994), Pena, Rubio, and Serna (1999), Foresi and Wu (2005), Zhang and Xiang (2008), Chang, Ren, and Shi

(2009), and Xing, Zhang, and Zhao (2010), among others. However, the literature pays little attention to the term structure of implied volatility (e.g., Campa & Chang, 1995; Xu & Taylor, 1994).

CHANG ET AL.

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