Volatility forecasts embedded in the prices of crude‐oil options

• Published date: 01 July 2020
• Author: Dudley Gilder,Leonidas Tsiaras
• Date: 01 July 2020
• DOI: http://doi.org/10.1002/fut.22114

J Futures Markets. 2020;40:1127–1159. wileyonlinelibrary.com/journal/fut

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1127

Received: 28 June 2018

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Accepted: 26 February 2020

DOI: 10.1002/fut.22114

RESEARCH ARTICLE

Volatility forecasts embedded in the prices of crude‐oil

options

Dudley Gilder

1

|Leonidas Tsiaras

2

1

Department of Accounting and Finance,

Cardiff Business School, Cardiff

University, Cardiff, UK

2

Department of Economics, Finance and

Entrepreneurship, Aston Business School,

Aston University, Birmingham, UK

Correspondence

Leonidas Tsiaras, Department of

Economics, Finance and

Entrepreneurship, Aston Business School,

Aston University, B4 7ET Birmingham,

UK.

Email: l.tsiaras@aston.ac.uk

Abstract

This paper evaluates the ability of alternative option‐implied volatility

measures to forecast crude‐oil return volatility. We find that a corridor

implied volatility measure that aggregates information from a narrow

range of option contracts consistently outperforms forecasts obtained by

the popular Black–Scholes and model‐free volatility expectations, as well

as those generated by a realized volatility model. This measure ranks fa-

vorably in regression‐based tests, delivers the lowest forecast errors under

different loss functions, and generates economically significant gains in

volatility timing exercises. Our results also show that the Chicago Board

Options Exchange's “oil‐VIX”index performs poorly, as it routinely pro-

duces the least accurate forecasts.

KEYWORDS

option‐implied volatility, realized variance, volatility forecasting

JEL CLASSIFICATION

C53; C58; G17

1|INTRODUCTION

In economic terms, crude‐oil is the most important traded commodity. Unsurprisingly, a wide range of economic

agents, from individual investors to policy makers, closely monitor its price and routinely attempt to make pre-

dictions about the future. Unlike standard financial assets, however, one salient feature of crude‐oilpricesisthat

they can experience dramatic shifts for reasons that are largely unrelated to global macroeconomic conditions,

such as OPEC policy changes or geopolitical instability in oil‐producing regions. It is therefore tempting to expand

the information set of standard time‐series models, which rely exclusively on the record of historical prices, with

measures that have “forward‐looking”features by construction.

Traded options appear as a natural candidate for this task. In theory, market efficiency dictates that

their prices should instantaneously adjust to any piece of relevant information pertaining to their expiration

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This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided

the original work is properly cited.

© 2020 The Authors. The Journal of Futures Markets published by Wiley Periodicals, Inc.

horizon.

1

In practice, option‐implied measures have indeed shown remarkable forecast performance across a

variety of markets and asset classes. As evidenced by the voluminous literature, this is particularly true for

volatility forecasting.

2

,

3

However, given a panel of option prices, different measures of expected, risk‐neutral, return variation can be

explored, so empirical evidence contrasting the various alternatives are needed to proceed. In this paper, we attempt to

fill this gap for the case of crude‐oil volatility. We do so by comparing the forecast performance, using both statistical

and economic criteria, of various popular alternatives, such as the Black–Scholes at‐the‐money implied volatility

(ATMIV), the so‐called model‐free implied volatility (MFIV), and the Crude Oil Volatility Index (OVX) published by the

Chicago Board of Options Exchange (CBOE). More important, we investigate, for the first time in the commodities

literature, corridor implied volatility (CIV) measures introduced by Carr and Madan (1998) and Andersen and Bon-

darenko (2007) and obtain very promising results.

The main strand of the crude‐oil volatility forecasting literature focuses on the performance of models belonging

either to the GARCH family, introduced by Bollerslev (1986), or those based on realized variance measures, notably the

heterogeneous autoregressive (HAR) model of Corsi (2009) and its extensions. Sadorsky (2006) finds that simple

GARCH models perform better than more complicated alternatives such as bivariate GARCH, vector autoregression,

and state‐space models. Kang, Kang, and Yoon (2009) compare various GARCH models with a particular focus on those

that exhibit long memory. More recently, Sévi (2014) and Prokopczuk, Symeonidis, and Wese (2016) utilize high

frequency returns and compare the original HAR model of Corsi (2009) with its variants that separately model the

continuous and discontinuous variance components. Interestingly, both studies find that jump decompositions do not

outperform the simple HAR model in terms of out‐of‐sample forecast accuracy.

Commencing with Latané and Rendleman (1976), there is a large collection of papers examining the information

content of option‐implied volatilities for the purpose of forecasting, with a handful of papers focusing on crude‐oil.

Naturally, early studies focused on producing forecasts using information in the ATMIV. Day and Lewis (1993) were

the first to examine this measure and found that ATMIV‐based forecasts encompass those generated by GARCH and

EGARCH models. Szakmary, Ors, Kim, and Davidson (2003) also compared ATMIV with GARCH‐based forecasts for

35 different assets, including crude‐oil, and found that ATMIV was superior in their forecasting comparisons. Similarly,

Martens and Zein (2004) find that option‐implied forecasts rank favorably against GARCH alternatives, although the

best models are those that combine both option‐implied and high‐frequency return information. Agnolucci (2009) also

favors models that combine GARCH and option‐implied forecasts, however, the former appear to be more accurate

than the latter in individual forecast comparisons.

While the early literature has examined the information content of Black–Scholes implied volatilities calculated

from different strikes and maturities (Beckers, 1981; Chiras & Manaster, 1978; Fung, Lie, & Moreno, 1990; Gemmill,

1986; Trippi, 1977) the consensus is that the simple ATMIV of a contract expiring as close to the forecast horizon

appears to provide the most reliable results. More recently, ATMIV forecasts have been compared to model‐free

volatility expectations that have a number of appealing theoretical properties.

4

The empirical evidence, however, has

produced inconclusive results. Jiang and Tian (2005) study the S&P500 index and find MFIV to be more informative

than ATMIV, while the opposite conclusion is reached by Andersen and Bondarenko (2007) for the same underlying

asset. Taylor, Yadav, and Zhang (2010) examine individual U.S. stocks and report that ATMIV provides more accurate

volatility forecasts than its model‐free counterpart. Finally, in their study of three energy markets, Prokopczuk and

Simen (2014) find that MFIV is more informative than ATMIV in predicting either crude‐oil, heating oil, or natural gas

volatility. They also find that a simple adjustment for volatility risk‐premia enhances the forecast performance of all

option‐implied measures.

When the task at hand is to predict future return variation MFIV is not without shortcomings. This is mainly for two

reasons. First, some options included in the calculation of this measure (such as deep out‐of‐the money puts for the case

of equities) tend to be very sensitive to volatility risk‐premia fluctuations. This can introduce substantial variation in the

1

Melick and Thomas (1997) provide an insightful study of how the option‐implied probability distributions of oil prices reflected market commentary

during the first Gulf War.

2

See Christoffersen, Jacobs, and Chang (2013), for a recent review of literature concerning the forecasting performance of various option‐implied

measures, including volatility.

3

Although, strictly speaking, this paper focuses on forecasting variance, we will use the terms “volatility”and “variance”interchangeably.

4

As shown in Carr and Madan (1998), Demeterfi, Derman, Kamal, and Zou (1999), and Britten‐Jones and Neuberger (2000), MFIV is a, risk‐neutral,

ex ante expectation of future return variation and, unlike the Black–Scholes implied volatilities, can be directly obtained from observed option price

data without assuming a particular option pricing model.

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GILDER AND TSIARAS

option‐implied measures that is largely unrelated to the forecast target, namely integrated variance (IVAR). Second,

calculating MFIV requires that market prices of options with extreme strikes are observed. In practice, this means that

either some extrapolation scheme must be implemented, or that options beyond a certain strike range should be

excluded from the calculation.

The most popular estimates of MFIV measures are the volatility indices produced and published by CBOE, such as

the volatility index (VIX) for the case of the S&P500 and the OVX for the case of crude‐oil. CBOE's implementation

algorithm, which is common for both the VIX and OVX indices, adopts a liquidity‐based cut‐off point that determines

the range of options to be included in the MFIV measure calculation. The choice of this algorithm by CBOE has

recently attracted some criticism. Andersen and Bondarenko (2007) were the first to note that the VIX is in fact an ex

ante measure of corridor integrated variance (CIVAR), rather than IVAR. In a comprehensive empirical study,

Andersen, Bondarenko, and Gonzalez‐Perez (2015) use high‐frequency option data and report that the VIX calculation

method introduces systematic biases to the extracted measure, including artificial jumps, which become particularly

pronounced during periods of market stress. From a different viewpoint, Griffin and Shams (2018) put forth evidence

pointing toward market manipulation of the VIX futures market. In essence, this is facilitated by CBOE's adopted cut‐

off algorithm, as speculators can temporarily boost the liquidity of deep out‐of‐the money S&P 500 options, increasing

the level of the VIX just before the settlement price for VIX futures is determined. Given that the same methodology is

used to calculate both the VIX and OVX indices, all the above raise reasonable concerns regarding the informational

efficiency of OVX‐based forecasts. In addition, since the popularity of volatility indices has recently become widespread

in the finance industry, a comparison between the OVX and other option‐implied alternatives appears to be long

overdue.

Our work builds on the study of Andersen and Bondarenko (2007) who explore an alternative measure of ex ante

risk‐neutral expectation of volatility, the so‐called CIV. Similar to the MFIV, and unlike the Black–Scholes model, this

measure aggregates volatility information from several options and does not depend on a particular option pricing

model. However, the extracted measure is not a risk‐neutral expectation of IVAR but CIVAR, that is return variation

accumulated only when the asset price lies within a corridor of two prespecified price levels. The advantage of this

approach is that one can select a corridor width that, while containing a wide‐range of option prices, excludes those

with extreme strikes, avoiding both price extrapolations and liquidity‐driven cut‐off points that may influence the

reliability of the extracted measure. Moreover, since each corridor corresponds to a different range of option data, one

can explore CIV measures that may be less sensitive to volatility risk‐premia fluctuations.

5

The contribution of this paper is threefold. First, we examine the forecast performance of CIV measures vis‐

à‐vis a collection of competing alternatives, including HAR,MFIV,OVX,andATMIVforecasts,forthecaseof

crude‐oil. Our paper builds, but significantly expands, on the work done by Prokopczuk and Simen (2014)who

compare the performance of MFIV and ATMIV forecasts. Besides considering additional option‐implied measures,

our study also includes models that utilize high‐frequency return information, while forecasts are ranked using

both statistical and economic criteria. Second, we evaluate volatility forecasts for the case of the United States Oil

Fund (USO), a exchange‐traded fund (ETF) that attempts to track the price of West Texas Intermediate light sweet

crude‐oil. Considering this alternative, yet closely related, target quantity, enables us to further scrutinize our

earlier findings. Moreover, to the best of our knowledge, we are first to construct and evaluate option‐implied

forecasts for this data set. Third, we provide the first empirical evaluation of the OVX index, used in the forecasting

study of Haugom, Langeland, Molnár, and Westgaard (2014), against other option‐implied alternatives. We do so

for both crude‐oil forecasts, which are more important in applied practice, as well as for USO volatility forecasts,

whichenablemorereliablemethodologicalcomparisons.ThisisbecauseUSOoptionsconstitutethebasisforthe

OVX calculation.

Our empirical results provide insights on a number of issues. We find that a particular CIV measure, that uses a

relatively narrow range of option prices, consistently ranks favorably against all other competing measures using a

variety of statistical and economic criteria. In particular, model forecasts that utilize this measure achieve the highest R

2

in Minzer‐Zarnowitz regressions, remain significant in encompassing regression tests, and deliver the most accurate

forecasts under both the symmetric and asymmetric loss functions we consider. Moreover, volatility timing exercises

show that utilizing this measure results in significant economic gains. The superior performance of this narrow CIV

5

For the case of the S&P 500, Dotsis and Vlastakis (2016) decompose MFIV into various corridor components and show that, indeed, each CIV

measure reflects different risk premia.

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