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Option implied ambiguity and its information content: Evidence from the subprime crisis

  • S.I.: Financial Economics
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“In abnormal times...when the hypothesis of an indefinite continuance of the existing state of affairs is less plausible than usual...the market will be subject to waves of optimistic and pessimistic sentiment, which are unreasoning and yet in a sense legitimate where no solid basis exists for a reasonable calculation.”

Keynes (1936)

Abstract

This paper studies option investors’ tendency to deviate from risk-neutrality around extreme financial events. We incorporate ambiguity into Black–Scholes theory and analyze the lead–lag association between option and stock markets during 2006–2008. Our findings from the Standard and Poor’s 500 index options reveal that investors’ option implied ambiguity moderates the lead–lag relationship between implied and realized volatility. We find that implied ambiguity contains predictive realized volatility information (beyond constant and stochastic implied volatilities), and that implied volatility is a less biased predictor of realized market variance when accounting for ambiguity in option pricing. We are also able to track changing investors’ ambiguity perceptions (pessimism or optimism) prior to severe volatility events and document shifts in ambiguity aversion among put option holders in the period leading to the fall 2008 global market crash. Our results hold under multiple-priors and Choquet ambiguity specifications.

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Notes

  1. Here we view Choquet ambiguity as a type of Knightian uncertainty, considering ambiguity as a dimension of uncertainty beyond probabilistic risk that can be estimated under a partial ignorance framework using Choquet expected utility (CEU) and Choquet Brownian motions. The words (Knightian) uncertainty and ambiguity are used interchangeably (De Palma et al. 2008; Guidolin and Rinaldi 2013). Alternative frameworks for representing ambiguity include multiple-priors expected utility (MEU) (e.g., Nishimura and Ozaki 2007; Riedel 2009) and robust control theory (e.g., Liu et al. 2005; Marzban et al. 2015). Throughout the paper, we study multiple-priors ambiguity as a special case of Choquet uncertainty.

  2. We go beyond descriptive observations by measuring and highlighting empirically the information content of investors’ ambiguity aversion, via the IV–RV linkage, in derivatives markets.

  3. Put options are examined in this research because they represent a form of insurance against losses for investors and are, therefore, suitable for our study of ambiguous behavior in uncertain times. Although our qualitative conclusions hold for call options holders, studying call option investments is out of the scope of this paper.

  4. Equation (1) also allows for more than one asset price S in the economy under ambiguity and implies uncertainty in bid and ask spreads (De Waegenaere and Wakker 2001).

  5. We assume, for simplicity, that ambiguity does not yet have an impact on equilibrium interest rates. This corresponds to cases where shocks in \(S_{t}\) are not yet correlated \((\rho _{2} = 0)\) to those of the economic output rate or where the latter is simply deterministic, as highlighted by Faria and Correia-da-Silva (2012) in their general equilibrium framework under ambiguity.

  6. This results from \(\frac{d\xi }{\xi }=f\left( {\xi ,S} \right) dt+g\left( {\xi ,S} \right) dW\) (see Harrison and Kreps 1979) and the characteristics of W in the Choquet ambiguity universe. The functions g and f help derive the ambiguity-adjusted formula for the pricing kernel.

  7. This implies that \(mg\left( {\xi ,S} \right) dt+\left( {s-1} \right) g\left( {\xi ,S} \right) dZ=0\), and that the market kernel is not equal to the marginal utility level. This results from market incompleteness that occurs during depressions or when the states of the world are not known (perfect hedging is no longer feasible under such conditions).

  8. \(\delta \) is introduced in the dt component of Eq. (1), replacing the drift term with \(\upmu -\delta \).

  9. Our conclusions are unchanged if series of shorter maturity contracts are selected over the 2006–2008 period.

  10. The significance of the IC variable is also maintained after controlling for realized skewness and kurtosis in the regressions.

Abbreviations

BS:

Black–Scholes

BSIV:

Black–Scholes risk-neutral implied volatility

BSIV \(\times \) IC:

Interaction between BSIV and IC

CBOE:

Chicago board options exchange

CDS:

Credit default swaps

CEU:

Choquet expected utility

IC:

Option implied ambiguity

ICBSIV:

Ambiguity-adjusted implied volatility (BSIV \(\times \) IC)

II:

Investors intelligence

IV:

Implied volatility

\(\hbox {IV}_{\mathrm{c}}\) :

Ambiguity-based implied volatility

MEU:

Multiple-priors expected utility

NW:

Newey–West

OTM:

Out of the money

RV:

Realized volatility

\(\hbox {s} \times \hbox {BSIV}\) :

Choquet-based implied volatility

SPX:

S&P 500 index options

SV:

Stochastic volatility

\(\hbox {SV} \times \hbox {IC}\) :

Interaction between SV and IC

VIX:

CBOE implied volatility index

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Acknowledgments

We thank the editors and the anonymous referees for their constructive comments and suggestions. Thanks are also due to Richard Arnott, Mark Clatworthy, Colin Clubb, Paul Guest, George Nishiotis, and Rafal Wojakowski for their helpful comments on earlier versions of this work. The author Lenos Trigeorgis is the Bank of Cyprus Chair Professor of Finance at the University of Cyprus.

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Authors and Affiliations

  1. Department of Management, King’s College London, University of London, Franklin-Wilkins Building, 150 Stamford Street, London, SE19NH, UK

    Tarik Driouchi & Raymond H. Y. So

  2. Department of Accounting and Finance, University of Cyprus, 1678, Nicosia, Cyprus

    Lenos Trigeorgis

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  1. Tarik Driouchi
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Correspondence to Tarik Driouchi.

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Driouchi, T., Trigeorgis, L. & So, R.H.Y. Option implied ambiguity and its information content: Evidence from the subprime crisis. Ann Oper Res 262, 463–491 (2018). https://doi.org/10.1007/s10479-015-2079-y

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