Uncertainty and the volatility forecasting power of option‐implied volatility

• Author: Jun Sik Kim,Byounghyun Jeon,Sung Won Seo
• Published date: 01 July 2020
• DOI: http://doi.org/10.1002/fut.22116
• Date: 01 July 2020

J Futures Markets. 2020;40:1109–1126. wileyonlinelibrary.com/journal/fut © 2020 Wiley Periodicals, Inc.

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1109

Received: 1 September 2019

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Accepted: 10 March 2020

DOI: 10.1002/fut.22116

RESEARCH ARTICLE

Uncertainty and the volatility forecasting power of

option‐implied volatility

Byounghyun Jeon

1

|Sung Won Seo

2

|Jun Sik Kim

3

1

College of Business Administration,

Marquette University, Milwaukee,

Wisconsin

2

Department of Business Administration,

Konkuk University, Gwangjin‐gu, Seoul,

Republic of Korea

3

Division of International Trade, Incheon

National University, Yeonsu‐gu, Incheon,

Republic of Korea

Correspondence

Jun Sik Kim, Division of International

Trade, Incheon National University, 119

Academy‐ro, Yeonsu‐gu, Incheon 22012,

Republic of Korea.

Email: junsici@inu.ac.kr

Funding information

Incheon National University Research

Grant in 2016

Abstract

This study investigates the impact of uncertainty on the volatility fore-

casting power of option‐implied volatility. Option‐implied volatility is a

powerful predictor of future volatility, particularly during periods of high

uncertainty. This is consistent with option‐implied volatility being largely

determined by volatility‐informed traders (rather than directional traders)

when uncertainty is high. New volatility forecasting models that in-

corporate such interaction outperform benchmark models, both in‐and

out‐of‐sample. The new models also better predict future volatility during

the 2008 global financial crisis, for which benchmark models perform

poorly. The results are robust to alternative choices of benchmark models,

loss functions, and estimation windows.

KEYWORDS

implied volatility, realized volatility, uncertainty, volatility forecasting

JEL CLASSIFICATION

C13; C22; C53; C58

1|INTRODUCTION

Modeling the volatility process and forecasting volatility are crucial in economic and financial decision‐making pro-

cesses, such as asset pricing and risk management. Hence, many researchers have introduced their own versions of the

volatility forecasting model (Andersen, Bollerslev, & Diebold, 2007; Corsi, 2009; Forsberg & Ghysels, 2007; Patton &

Sheppard, 2015). Concurrent with the development of the options market, many studies document that implied

volatility provides superior information in predicting future volatility (Blair, Poon, & Taylor, 2001; Busch, Christensen,

& Nielsen, 2011; Christensen & Prabhala, 1998; Jiang & Tian, 2005). Owing to the convex payoff structure and

embedded leverage, the options market offers unique opportunities for informed traders to trade on their volatility‐

related information (Ni, Pan, & Poteshman, 2008). Therefore, combined with its forward‐looking nature, option‐implied

volatility provides independent and superior information on future volatility compared to historical stock market

volatility.

Recent volatility forecasting models step further and introduce time variation in the volatility forecasting power of

both option‐implied and historical volatility. Several studies consider time variation with respect to measurement error

(Bollerslev, Patton, & Quaedvlieg, 2016), the discrepancy between short‐and long‐term volatility (Li, Tsionas, &

Izzeldin, 2016), and investor sentiment (Seo & Kim, 2015).

In this paper, we introduce a new class of volatility forecasting models that allow the predictability of option‐implied

volatility to hinge on uncertainty. Uncertainty is a core concept in finance, accompanied by vast literature on its impact

on asset pricing and informed trading.

1

,

2

However, there is scant evidence of its effect on volatility forecasting. The

forward‐looking nature and active informed trading in the options market make it particularly interesting to investigate

how uncertainty influences informed trading in the options market, and hence the volatility forecasting power of

option‐implied volatility. We try to fill this gap in the literature by documenting the effect of uncertainty on the

predictive power of option‐implied volatility.

In this study, we focus on Knightian uncertainty, in line with Segal (1987) and Baltussen, Van Bekkum, and Van der

Grient (2018).

3

In this setting, the two key parameters (expected return and risk) of the stock return distribution are

unknown. The parameter values are individually drawn from parameter distributions. Hence, the uncertainty about

risk in this setting refers to the standard deviation of the risk parameter distribution. Therefore, a straightforward proxy

for uncertainty about risk would be the volatility‐of‐volatility (VoV), as introduced by Baltussen et al. (2018). VoV is

volatility in the option‐implied market volatility, and primarily measures uncertainty about volatility. It offers several

advantages over uncertainty measures based on surveys of analysts and professionals: it is ex ante, easy to compute,

available at a daily frequency, derived directly from market transactions, and circumvents the self‐selection problem

and optimism bias in analyst forecasts (McNichols & O'Brien, 1997). Therefore, VoV is a popular measure of un-

certainty about volatility (Andreou, Kagkadis, Philip, & Tuneshev, 2018; Borochin & Zhao, 2019; Cao, Vasquez, Xiao, &

Zhan, 2018; Dubinsky, Johannes, Kaeck, & Seeger, 2019; Hollstein, Nguyen, & Prokopczuk, 2019; Ruan, 2019).

Our empirical findings suggest that the volatility forecasting power of option‐implied volatility increases at high

levels of uncertainty measured by VoV. In a predictive time‐series regression of future volatility, the coefficient on the

interaction term between option‐implied variance and VoV is significantly positive. Furthermore, including the in-

teraction between implied variance (IV) and VoV increases the in‐sample adjusted R

2

by more than 1%. The out‐of‐

sample tests also confirm that incorporating uncertainty into the volatility forecasting models significantly improves

model fit. These improvements in the empirical analyses are robust to using the implied volatility of volatility index

(VVIX) as a different measure of uncertainty about risk. In addition, incorporating uncertainty into the benchmark

models significantly improves both in‐and out‐of‐sample fit during the financial crisis, during which the benchmark

models perform poorly. Lastly, the results hold across alternative choices of benchmark models, loss functions, and

estimation windows.

A noteworthy regularity in our result is that option‐IV becomes more informative about future realized variance

(RV) during periods of high uncertainty compared to other periods. We propose the following two channels. First,

uncertainty about volatility increases the information asymmetry about future volatility, which attracts more volatility‐

informed trading in the options market. Under severe information asymmetry, volatility‐informed traders have strong

incentives to exploit their information in the options market to maximize their profits using a convex payoff structure

and embedded leverage. Therefore, implied volatility reflects the expectations of volatility‐informed investors well.

Second, high uncertainty drives directional traders out of the options market, hence reducing noise in implied volatility.

Directional trading is another prime trading strategy in the options market that distorts options prices (e.g., put‐call

parity violation) and adds significant noise to implied volatility (Cremers & Weinbaum, 2010; Easley, O'Hara, &

Srinivas, 1998). Both theoretical (Capelle‐Blancard, 2001) and empirical works (Chakravarty, Gulen, & Mayhew, 2004;

Han, Kim, & Byun, 2017) support the notion that directional traders move away from the options market during periods

of high uncertainty. In sum, under high uncertainty, implied volatility is largely determined by volatility‐informed

traders (rather than directional traders), which makes it highly informative of future volatility.

1

Knightian uncertainty is a situation where each agent has their own prior belief on an unknown parameter, where in risk, theta is known. Al‐Najjar

and Weinstein (2015) suggest that the difference between imperfect information and Knightian uncertainty is that uncertainties are not empirical.

First, beliefs about uncertain events cannot be objectively tested to determine whether they are right or wrong. Second, it is hard to estimate the

impact using traditional econometric methods. A standard assumption is rational expectations which identifies beliefs with the observed empirical

frequencies. While this assumption offers considerable advantages, it also rules out subjective model‐uncertainty as a factor in decisions. Knightian

uncertainty is often times approached using Bayesian framework and they are consistent with each other. If agents update their subjective belief on

unknown parameters, it would be consistent with Bayesian learning (Halevy & Feltkamp, 2005; Weitzman, 2007).

2

Studies such as those by Buraschi and Jiltsov (2006), Andersen, Ghysels, and Juergens (2009), Beber, Breedon, and Buraschi (2010); Buraschi,

Trojani, and Vedolin (2013), and Buraschi, Trojani, and Vedolin (2014) investigate the relation between uncertainty and asset pricing in the financial

markets, such as the stock, options, currency, and bond markets.

3

Other studies examine different types of uncertainty. For example, Segal, Shaliastovich, and Yaron (2015) decompose aggregate uncertainty into

“good”and “bad”volatility components, where the former is the volatility associated with positive innovations to macroeconomic quantities, such as

output, consumption, and earnings, and the latter is the volatility associated with negative innovations to macroeconomic quantities. They compute

the positive and negative realized semivariance based on the growth rate of output. Therefore, their measure captures the risk of future macro-

economic growth, rather than the uncertainty about volatility. Thus, uncertainty in Segal et al. (2015) represents a different aspect of uncertainty than

the one we investigate here.

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JEON ET AL.