Forecasting using alternative measures of model‐free option‐implied volatility

• Author: Marwan Izzeldin,Xingzhi Yao
• Published date: 01 February 2018
• Date: 01 February 2018
• DOI: http://doi.org/10.1002/fut.21881

Received: 12 April 2017

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Accepted: 20 August 2017

DOI: 10.1002/fut.21881

RESEARCH ARTICLE

Forecasting using alternative measures of model-free

option-implied volatility

Xingzhi Yao

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Marwan Izzeldin

Department of Economics, Lancaster

University Management School,

Lancaster, UK

Correspondence

Xingzhi Yao, Department of Economics,

Lancaster University Management School,

Lancaster, LA1 4YX, UK.

Email: x.yao@lancaster.ac.uk

Funding information

Economic and Social Research Council,

Grant number: ES/J500094/1

This paper evaluates the performance of various measures of model-free implied

volatility in predicting returns and realized volatility. The critical role of the

out-of-the money call options is highlighted through an investigation of the relevance

of different components of the model-free implied volatility. The Monte Carlo

simulations show that: first, volatility forecasting performance of various measures

can be enhanced by employing an interpolation-extrapolation technique; second, for

most measures considered, gains in their predictive power for future returns can be

obtained by implementing an interpolation procedure. An empirical application using

SPX options recorded from 2003 to 2013 further illustrates these claims.

JEL CLASSIFICATION

C63, G13, G17

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INTRODUCTION

In an efficient market, the option price embodies all available useful information about future movements of the underlying asset.

Hence, traders and hedge fund managers are primarily interested in option-implied volatility when making financial decisions.

As a natural forecast of return variation over the remaining life of the relevant option, option-implied volatility has been

frequently used in forecasting future volatility, see Poon and Granger (2003) for an extensive review of the studies on this topic.

As opposed to the Black–Scholes (BS) implied volatility, model-free option-implied volatilities have gained substantial

popularity because, relying upon no particular parametric model, they avoid potential mis-specification problems. See, for

example, Britten-Jones and Neuberger (2000), Carr and Wu (2006), and Taylor, Yadav, and Zhang (2010).

One of the most widely adopted measu res of model-free option-impli ed volatility is the VIX volatility index,

disseminated by the Chicago B oard of Options Exchange (CBO E). The VIX provides a measure of the expec ted value of the

S&P 500 return variation under the risk-neutral measure and is designed to closely mimic the model-free implied volatility

(MFIV). Derived by Br itten-Jones and Neuberge r (2000), the MFIV is defined as an integral of cross-section of ou t-of-the

money (OTM) European style pu t and call options over an inf inite range of strikes for the given maturity. Jiang and Tian

(2005) show that the MFIV is a more ef ficient forecast for future r ealized volatility than the BS im plied volatility and the

historical realized volatil ity. However, Andersen and Bond arenko (2007) argue that the MFIV and VIX are biased forecasts

of future volatility since th ey contain non-trivial and time-varying risk premiu ms. As a more important part of their empirical

study, Andersen and Bondare nko (2007) investigate the pr operties of the corridor imp lied volatility index (CX ), which is

obtained from the MFIV by trunc ating the integration doma in between two barriers. Bei ng less sensitive to variati on in the

market variance risk premiu m, the CX with the narrowest corrid or width is found to dominate other impl ied volatility

measures in the work of Ander sen and Bondarenko (2007). An other advantage of the CX is th at it is constructed only ove r

intervals of the risk-neutr al density (RND) where price quo tes are directly observable . By contrast, the computatio n

J Futures Markets. 2018;38:199–218. wileyonlinelibrary.com/journal/fut © 2017 Wiley Periodicals, Inc.

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requirements for derivin g the MFIV are not satisfied by the existing data as options are tr aded only over a finite ran ge of

strikes. Andersen, Bondar enko, and Gonzalez-Perez (20 15) further improve the cons truction of the CX by adopting th e

concept of an invariant cover age across time, which ensure s that the CX is coherent in the ti me series dimension. As

compared with the VIX, which is based upon stron gly time-varying coverage of the tails of the RND, t he CX uses a consistent

range of strikes, which serves as a more accurate volatility indicator over time.

In addition to the use of implied volatilities in forecasting future volatility, prior studies also indicate that the VIX may carry

some predictive power for future returns on stock market indices. For example, Giot (2005) finds that future returns are always

positive (negative) for very high (low) levels of the VIX. This accords with the work of Guo and Whitelaw (2006) who provide

evidence for the positive relationship between market returns and implied volatilities. The positive relationship between the VIX

and future returns is also documented in Banerjee, Doran, and Peterson (2007) who suggest that both levels and innovations of

the VIX are significantly related to future returns. That finding is indicative of a negative volatility risk premium, which is

consistent with Ang, Hodrick, Xing, and Zhang (2006) where stocks with high past sensitivities to the innovation in the VIX

display on average future decreasing returns. The evidence that the VIXis a priced risk factor in the time series of returns helps to

explain why the VIX may exhibit predictive power for future returns. Although a substantial empirical literature is devoted to the

investigation of risk-return relations (see, e.g., the discussion in Rossi & Timmermann (2010), and the many references therein),

most rely on the VIX as a directly observable proxy for risk. Other measures of model-free option-implied volatility are rarely

considered.

Despite the increasing popularity of the VIX, measurement errors in its construction have been noted by Jiang and Tian

(2005). The common problem inherent in the computation of the VIX as well as other measures of model-free implied volatility

is that only a discrete set of strikes is actually traded in the market and that very low and high strikes are usually absent. To

account for measurement errors induced by the limited number of strikes, Jiang and Tian (2005) apply the cubic spline method to

interpolate between existing strikes and exploit a flat extrapolation scheme to infer option prices beyond the truncation point.

Andersen and Bondarenko (2007) address the issue induced by the discrete set of strikes via the positive convolution

approximation method proposed by Bondarenko (2003). Although interpolation and extrapolation techniques are widely

accepted, it remains unclear how such techniques affect the performance of implied volatilities in predicting future returns and

realized volatility. In addition, there appears to be no consensus on the roles played by the OTM call and put options in the

forecast of future volatility and returns. Jackwerth (2000), Jones (2006), and Bates (2008) suggest that the OTM put options may

be irrelevant to known risk factors affecting stock returns. Using a cubic spline interpolation and flat extrapolation methods,

Dotsis and Vlastakis (2016) also find that the OTM put options, especially deep OTM puts, do not contain important information

with respect to equity volatility risk. They also show that the OTM call options subsume all useful information embedded in the

OTM puts for forecasting future realized volatility. However, Andersen, Fusari, and Todorov (2015) show that the left tail risk,

driving a substantial part of the OTM put option dynamics, exhibits strong predictive power for future excess market returns over

long horizons.

Against this background, thi s study examines the performan ce of various model-free opti on-implied volatilitie s in

predicting future returns and volatility and contr ibute to the existing lite rature in the following way s. First, this paper is

among the first to provide sim ulation evidence to justif y the use of the interpolatio n/extrapolation procedu re for better

forecasting performance o f implied volatilities. The us efulness of this procedure is ve rified in both the simulation a nd

empirical studies. The adop tion of a stochastic volatil ity model with both jumps and vola tility risk premium in the pre sent

study mimics more closely the ob served data dynamics. This c an be seen as an extension of the work of Zhang, Taylo r, and

Wang (2013) where a simple square- root model of Cox, Ingersoll, and R oss (1985) is employed to investig ate the number of

options upon the informatio n content of the MFIV in an in-s ample analysis. Distinct fro m Zhang et al. (2013), this paper

conducts comprehensive ou t-of-sample (OOS) volatili ty forecasts made by differ ent implied volatility measu res including

the MFIV.

Second, to ascertain the relevance of the OTM call and put options, this paper considers implied volatility measures

constructed entirely from the cross-section of OTM put (call) options and measures which discard the deep OTM put (call)

options. This is achieved by splitting the MFIV into different components with the use of different intervals of the cross-section

of OTM put and call option prices. Similar constructions of implied volatilities are conducted in Dotsis and Vlastakis (2016) who

examine the price of volatility risk in the cross-section of stock returns. With a different focus from that of Dotsis and Vlastakis

(2016), the present paper compares the fraction of the time-series variation in future returns that are explained by various

measures of implied volatility. Return predictability provided by implied volatilities is investigated in the pre- and post-crisis

periods, respectively. The impact of the recent financial crisis is accounted for since the crisis represents an informative period

during which uncertainty and risk aversion may have been more evident than the non-crisis period, see Hilal, Poon, and Tawn

(2011) and Bates (2012).

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