Are there gains from using information over the surface of implied volatilities?

• Author: Hai Lin,Biao Guo,Qian Han
• DOI: http://doi.org/10.1002/fut.21903
• Date: 01 June 2018
• Published date: 01 June 2018

Received: 19 June 2017

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Accepted: 27 November 2017

DOI: 10.1002/fut.21903

RESEARCH ARTICLE

Are there gains from using information over the surface of

implied volatilities?

Biao Guo

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Qian Han

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Hai Lin

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1

School of Finance, Renmin University of

China, Beijing, China

2

Wang Yanan Institute for Studies in

Economics, Xiamen University, Xiamen,

China

3

School of Economics and Finance,

Victoria University of Wellington,

Wellington, New Zealand

Correspondence

Hai Lin, School of Economics and Finance,

Victoria University of Wellington,

Wellington 6140, New Zealand.

Email: hai.lin@vuw.ac.nz

Funding information

National Natural Science Fund of China,

Grant numbers: 71471153, 71503254;

NNSFC Key Project, Grant number:

71631004

We investigate the out-of-sample predictability of implied volatility using the

information over the implied volatility surface. We show that implied volatility

surface is useful for the out-of-sample forecast of implied volatility up to 1 week

ahead. Trading strategies based on the predictability of implied volatility could

generate significant risk-adjusted gains after controlling for transaction costs.

Significant results also depend on the way of modeling implied volatility surface. We

then calibrate a two-factor stochastic volatility option pricing model to implied

volatility data. Results show that implied volatility is better explained by both long-

and short-term variance factors.

KEYWORDS

economic significance, implied volatility, out-of-sample forecast, two-factor stochastic volatility

model

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INTRODUCTION

Whether asset returns are predictable has been a longstanding research question in literature.

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On option market, Harvey and

Whaley (1992), Gonclaves and Guidolin (2006), Konstantinidi, Skiadopoulos, and Tzagkaraki (2008), Chalamandaris and

Tsekrekos (2010, 2011) and Neumann and Skiadopoulos (2013) find that option implied volatilities are statistically predictable.

However, the economic profits become insignificant once the transaction costs are accounted for. Literature documents a

disparity between statistical and economical significance of option market predictability.

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In this paper, we solve the disparity by using implied volatility surface information. The trading of the option market is

dominated by short-maturity options. Nevertheless, Bakshi, Cao, and Chen (1997) find that long-dated options have information

not readily available from short-dated options. Recently, Christoffersen, Jacobs, Ornthanalai, and Wang (2008) and

Christoffersen, Heston, and Jacobs (2009) proposed component volatility models, and decomposed stochastic volatility into

long- and short-term components. They find that component volatility models perform better than one-factor stochastic volatility

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See, for example, Fama and Schwert (1977), Fama and French (1988), Campbell and Shiller (1988), Kothari and Shanken (1997), Rapach et al. (2010,

2013), Pettenuzzo, Timmermann, and Valkanov (2014), Rapach, Ringgenberg, and Zhou (2016) on predicting stock returns; Keim and Stambaugh (1986),

Fama and French (1989), Greenwood and Hanson (2013), Lin et al. (2014), Lin, Wu, and Zhou (2017) on predicting corporate bond returns; and Fama

and Bliss (1987), Campbell and Shiller (1991), Cochrane and Piazzesi (2005), Goh, Jiang, Tu, and Zhou, (2012), Sarno, Schneider and Wagner (2016),

Gargano, Pettenuzzo, and Timmermann (2017), Lin, Liu, Wu, and Zhou (2017) on predicting Treasury bond returns.

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Similar disparity of statistical and economic significance on Treasury return predictability is documented in Thornton and Valente (2012).

J Futures Markets. 2018;38:645–672. wileyonlinelibrary.com/journal/fut © 2018 Wiley Periodicals, Inc.

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model. These findings suggest there exists useful information in the whole implied volatility surface. Bakshi et al. (1997),

Christoffersen et al. (2008, 2009) analyze the statistical significance. We extend their analysis to investigate the economic

significance of implied volatility surface, and document significant economic gains by using the information of implied volatility

surface.

We test whether incorporating the information of implied volatility surface can improve the prediction of implied volatility.

If both long- and short-maturity implied volatilities contain useful information, using the whole implied volatility surface

information will be able to improve the volatility forecast that is only based on one particular maturity information. We examine

14 models and compare their out-of-sample performance with that of the benchmark AR(1) model. These competing models

are two adapted Nelson and Siegel models used by Diebold and Li (2006) for Treasury securities and by Chalamandaris and

Tsekrekos (2011) for currency options, six time series models similar to Diebold and Li (2006), five combination models as in

Rapach, Strauss, and Zhou (2010) and a Mallows model averaging (MMA) combination as in Hansen (2007, 2008). We use the

implied volatility surface information of the at-the-money (ATM) options and the options with Δ0.40 and Δ0.60. We choose call

option in our main analysis, and use put option as a robustness check. We find that, historical surface information plays a

significant role in the prediction of implied volatilities. When daily data are used to forecast the 30-day implied volatility 1 day

ahead and 5 days ahead, the best out-of-sample R

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value is as high as 7.39% and 7.64%, respectively.

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Results are significant

across almost all maturities. Our results reveal the importance of using the whole implied volatility surface information.

However, these models lose their predictive power beyond a week, suggesting that only the historical information within 1 week

of the forecast date is important for the short-term forecast of index option market.

To examine whether the predictability has economic value, we construct a trading strategy based on a forecast by each model,

and compare the portfolio performance with that of the benchmark AR(1) model. Using the gain on Leland's alpha (Leland,

1999) as the performance measure, we find that those models that utilize information from the entire surface generate significant

economic profits up to 5 days ahead even after transaction costs are considered. For example, when daily data are used, the

trading strategy based on the 1-day-ahead forecast by the VAR(1) model of volatility change (VARC) generates a gain on

Leland's alpha of 11.13% relative to the benchmark, and is significant at the 1% level. The trading strategy based on the 5-day-

ahead forecast by the VAR(1) model of volatility change (VARC) generates a gain on Leland's alpha of 2.13% relative to the

benchmark, and is significant at the 10% level. Results are robust to the impact of transaction cost. This finding distinguishes our

study from most other literature that finds no predictability of the option market after considering transaction costs.

Our findings are robust over time and over different options. A sub-sample analysis using data during the recent 2007–2009

financial crisis period finds that the predictability still exists during the crisis. Implied volatilities can still be predicted 5 days

ahead. Moreover, their economic significance of 1-day-ahead forecast becomes stronger during the crisis. Analysis using put

option data and data with a broader range of Δfurther confirms our main results.

In order to explain why implied volatility surface information helps improve the forecast, we estimate a two-factor stochastic

volatility option pricing model to extract a long-term and a short-term variance factor. Regressions of option implied volatilities

on these two factors reveal that both variance factors are important to explain the time variations of implied volatility. Long-

maturity implied volatilities are more associated with the long-term variance factor, while short-maturity implied volatilities are

more related to the short-term variance factor. Both long- and short-maturity implied volatilities contain useful information of

the implied volatility term structure. We are able to provide a better prediction by using them jointly.

Our study contributes to the literature in several ways. Our findings shed light on volatility modeling. We evaluate an

extensive set of 14 models. Our finding that the whole implied volatility surface provides useful information in forecasting

implied volatility suggests that a one-factor model is not sufficient for volatility modeling. In this regard, we provide empirical

evidence consistent with the emerging component volatility models.

We document both statistical and economic significance of option market predictability using the information of implied

volatilitysurface. This finding is different fromliterature that documents significantstatistical predictabilitybut fails to uncover the

economic significance. This finding provides new insights to the economic profit by the predictability of implied volatility.

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Egloff, Leippold, and Wu (20 10) and Johnson (2017) show that besides leve l, slope also helps predict the im plied

variance. We differ from them by co nsidering more flexible models to use the information contained in the surface of implied

volatilities. As a robustn ess check, we also compare the 14 mode ls with the two-factor model that uses level and slope as th e

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These results are higher than or comparable to studies on the predictability of other financial markets. See, for example, Gargano et al. (2017) on

Treasury return predictability, Lin et al. (2014) and Lin, Wu, et al. (2017) on corporate bond return predictability, and Rapach et al. (2010), Pettenuzzo

et al. (2014) and Rapach et al. (2016) on stock return predictability.

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Galai (1977), Chiras and Manaster (1978), Poon and Pope (2000) and Hogan, Jarrow, Teo, and Warachka, (2004) also find significant excess returns of

option trading strategies even when transaction costs are considered.

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