Improving Volatility Forecasts Using Market‐Elicited Ambiguity Aversion Information

• DOI: http://doi.org/10.1111/fire.12172
• Date: 01 November 2018
• Published date: 01 November 2018

The Financial Review 53 (2018) 705–740

Improving Volatility Forecasts Using

Market-Elicited Ambiguity Aversion

Information

Raymond H.Y. So∗and Tarik Driouchi

King’s College London

Abstract

Distinguishing between risk and uncertainty, this paper proposes a volatility forecasting

framework that incorporates asymmetric ambiguity shocks in the (exponential) generalized

autoregressive conditional heteroskedasticity-in-meanconditional volatility process. Spanning

25 years of daily data and considering the differential role of investors’ ambiguity attitudes

in the gain and loss domains, our models capture a rich set of information and provide more

accurate volatility forecasts both in-sample and out-of-sample when compared to ambiguity-

free or risk-based counterparts. Ambiguity-based volatility-timing trading strategies confirm

the economic significance of our proposed framework and indicate that an annualized excess

return of 3.2% over the benchmark could be earned from 1995 to 2014.

Keywords: decision theory, model uncertainty, ambiguity, volatility

JEL Classifications: G41, D81, D91

∗Corresponding author: King’s Business School, King’s College London, University of London, Bush

House, 30 Aldwych, London WC2B 4BG, United Kingdom; Phone: +44 020 78484943; E-mail:

raymond.so@kcl.ac.uk.

We thank the editor and an anonymousreferee for constructive and useful comments.

C2018 The Eastern Finance Association 705

706 R. H. Y. So and T. Driouchi/The Financial Review 53 (2018) 705–740

1. Introduction

Pioneered by Engle (1982), the autoregressive conditional heteroskedasticity

(ARCH) volatility modeling approach has revolutionized the way we predict volatil-

ity and allowed understanding time-varying volatility under different assumptions.

Engle’s (1982) seminal approach in modeling conditional volatility has been ex-

tended to the generalized ARCH (GARCH; Bollerslev, 1986), exponential ARCH

(E[G]ARCH; Nelson, 1991), and GJR-(G)ARCH models (Glosten, Jagannathan and

Runkle, 1993). In recent years, an important stream of research concerned with the

notion of ambiguity, as uncertainty beyond probabilistic risk, has emerged to high-

light the relevance and significance of model uncertainty in asset pricing, volatility

prediction, policy evaluation, and decision making (e.g., Manski, 2000; Cao, Wang

and Zhang, 2005; Brock, Durlauf and West,2007; Agliardi and Agliardi, 2009; Easley

and O’Hara, 2009; Kast, Lapied and Roubaud, 2014). The concept of uncertainty and

its distinction from risk was highlighted almost a century ago by Knight (1921),

was further conceptualized by Keynes (1921, 1937), and corroborated by Ellsberg

(1961) in his famous thought experiments on individual decision making under am-

biguity. Although ambiguity is widely recognized and theorized by researchers in the

context of financial markets (e.g., Gilboa and Schmeidler, 1989; Chateauneuf, Kast

and Lapied, 1996; Cao, Wang and Zhang, 2005; Handel, Misra and Roberts, 2013),

empirical work linking model uncertainty to volatility modeling is still scarce (e.g.,

Buraschi and Jiltsov,2006; Anderson, Ghysels and Juergens, 2009; Fan and Mancini,

2009; Driouchi, Trigeorgis and So, 2018). This is due to the inherent difficulties in

quantifying ambiguity empirically.

Motivatedby the need to quantify ambiguity and assess the potential implications

of model uncertainty in volatility prediction, this paper investigatesthe empirical rela-

tion between ambiguity attitudes and risk in financial markets and highlights the value

of incorporating ambiguity in GARCH volatility forecasts. In a recent paper,Driouchi,

Trigeorgis and So (2018) study the lead-lag relation between ambiguity implied by

option prices and realized volatility around the subprime crisis in a standard historical

variance setting and demonstrate that forward-looking ambiguity can be important in

volatility prediction especially in uncertain times (i.e., 2006–2008). In their effort to

estimate the impact of uncertainty on expected returns, Anderson, Ghysels and Juer-

gens (2009) examine the effect of uncertainty on conditional volatility as a robustness

check. However,their study only focuses on quarterly data, as limited by the availabil-

ity of professional forecasters’ survey data, and does not provide information on how

uncertainty affects conditional volatility in higher frequency settings (e.g., daily).

Also related, Fan and Mancini (2009) show how accounting for learning and model

misspecification in option pricing can minimize empirical pricing errors and improve

volatility prediction. They validate their approach using option pricing data for the

2002–2004 period. No study highlights the role of ambiguity aversion, as a behavioral

construct, in volatility forecasting over an extensive time window in- and out-of-

sample and using a large data set of option prices in the context of GARCH volatility.

R. H. Y. So and T. Driouchi/The Financial Review 53 (2018) 705–740 707

We fill this gap in research by examining the relation between investors’ atti-

tudes toward ambiguity,as inferred from market-traded option prices, and conditional

volatility over the 1990–2014 period. Specifically, we extract investors’ attitudes to-

ward ambiguity from Standard & Poor’s (S&P) 500 index options using a modified

option pricing formula under ambiguity and account for ambiguity innovations in

our GARCH volatility forecasts. This approach allows us to capture and quantify

the ambiguity attitudes of sophisticated options investors/traders on a real-time basis.

Our paper differs from that of Driouchi, Trigeorgisand So (2018) in that we explicitly

incorporate ambiguity innovations in the GARCH methodology, control for down-

side and upside markets (i.e., gains vs losses), and assess economic significance and

forecasting accuracy in- and out-of-sample over the entire 1990–2014 period. Not

concerned with the GARCH apparatus, Driouchi, Trigeorgis and So (2018) focus

on the subprime crisis and the incremental information content of ambiguity implied

from put option prices over 2006–2008 in a standard historical variance setting. By al-

lowing asymmetric1uncertainty shocks in the GARCH conditional volatility process

for gains and losses, we show that option market ambiguity attitudes (OMAA) are

quantitatively important in determining the subsequent level of conditional volatility.

Our analysis reveals a strong relation between OMAA and ex post conditional volatil-

ity over a quarter century of daily data. Ambiguity aversion is positively associated

with ex post conditional volatility in the gain domain, while negatively associated

with ex post conditional volatility in the loss domain. This special S-shape relation

has been prominent in the behavioral economics, decision theory, and psychology

literatures concerned with agents’ decision-making behavior. We unveil it in the con-

text of financial markets and GARCH volatility forecasting. Our results are robust to

a range of forecasting tests (e.g., in-sample, out-of-sample, superior predictive ability

[SPA], and economic significance) and various modeling specifications.

Earlier studies suggest that the relation between an individual’s decision and

her ambiguity attitude may not be explained by a simple linear relation, especially

when considering emotional sensitivities to gains and losses (Tverskyand Kahneman,

1986; Thaler and Johnson, 1990; Thaler, Tversky, Kahneman and Schwartz, 1997;

Low, 2004). For example, Viscusi and Chesson (1999) explain how an individual’s

ambiguity attitude may shift from ambiguity aversion to ambiguity seeking (and

vice versa) under the fear and hope effects. Their work underlines the differential

role of ambiguity attitudes in the gain and loss domains. They suggest that in the

gain domain, subjects are more ambiguity averse for high probabilities of gains

but become more ambiguity seeking for low probabilities of gains. On the other

hand, in the loss domain, subjects are more ambiguity seeking for high probabilities

of loss and more ambiguity averse for low probabilities of loss. A similar shift in

1The asymmetric property of volatility has been well-documented. For example, Ewing and Malik (2010)

estimate volatility persistence in GARCH models by introducing an asymmetric structural break variable.

Tse (2016) finds that asymmetric volatility generates long-run skewness.