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

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.

[1]  M. Rieger,et al.  Can Ambiguity Aversion Solve the Equity Premium Puzzle? Survey Evidence from International Data , 2012, Cultural Finance.

[2]  Joan L. Walker,et al.  Risk, uncertainty and discrete choice models , 2008 .

[3]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[4]  Andrea Buraschi,et al.  Model Uncertainty and Option Markets with Heterogeneous Beliefs , 2006 .

[5]  Bing Han Investor Sentiment and Option Prices , 2005 .

[6]  Jörg Vorbrink American options with multiple priors in continuous time , 2011 .

[7]  David M. Kreps,et al.  Martingales and arbitrage in multiperiod securities markets , 1979 .

[8]  Timothy Cogley,et al.  Robustness and U.S. Monetary Policy Experimentation , 2008 .

[9]  Nina Boyarchenko Ambiguity Shifts and the 2007-2008 Financial Crisis , 2010 .

[10]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[11]  John D. Hey,et al.  The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity , 2010, Experiments in Economics.

[12]  Hersh Shefrin,et al.  A Behavioral Approach to Asset Pricing , 2005 .

[13]  Ambiguity Aversion and Asset Prices in Production Economies , 2014 .

[14]  Stephen L Taylor,et al.  The Information Content of Implied Volatilities and Model-Free Volatility Expectations: Evidence from Options Written on Individual Stocks , 2006 .

[15]  Gonçalo Faria,et al.  The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices , 2012 .

[16]  M. Subrahmanyam,et al.  When are Options Overpriced? The Black-Scholes Model and Alternative Characterizations of the Pricing Kernel , 1999 .

[17]  Umberto Cherubini,et al.  Fuzzy measures and asset prices: accounting for information ambiguity , 1997 .

[18]  H. B. Ameur,et al.  Optimal portfolio positioning under ambiguity , 2013 .

[19]  Tim Leung,et al.  Impact of risk aversion and belief heterogeneity on trading of defaultable claims , 2016, Ann. Oper. Res..

[20]  Christian Gollier,et al.  Discounting with fat-tailed economic growth , 2008 .

[21]  J. Doob Stochastic processes , 1953 .

[22]  P. Wakker Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle , 2001 .

[23]  E. Agliardi,et al.  Luigi Sereno The effects of environmental taxes and quotas on the optimal timing of emission reductions under Choquet-Brownian uncertainty Discussion , 2011 .

[24]  J. L. Ford,et al.  Information and ambiguity: herd and contrarian behaviour in financial markets , 2013 .

[25]  J. Fung The Information Content of Option Implied Volatility Surrounding the 1997 Hong Kong Stock Market Crash , 2007 .

[26]  A. D. Waegenaere,et al.  Choquet pricing and equilibrium , 2003 .

[27]  J. Jackwerth Recovering Risk Aversion from Option Prices and Realized Returns , 1998 .

[28]  Luis A. Seco,et al.  Using equity options to imply credit information , 2011, Ann. Oper. Res..

[29]  Silvia Muzzioli,et al.  A multiperiod binomial model for pricing options in a vague world , 2004 .

[30]  I. Drechsler,et al.  Uncertainty, Time-Varying Fear, and Asset Prices , 2013 .

[31]  D. Roubaud,et al.  Modelling under ambiguity with dynamically consistent Choquet random walks and Choquet'Brownian motions , 2014 .

[32]  Gonçalo Faria,et al.  A closed-form solution for options with ambiguity about stochastic volatility , 2014 .

[33]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[34]  Jun Liu,et al.  An Equilibrium Model of Rare Event Premia , 2002 .

[35]  Tao Li Heterogeneous Beliefs, Asset Prices, and Volatility in a Pure Exchange Economy , 2006 .

[36]  David Kelsey,et al.  E-Capacities and the Ellsberg Paradox , 1999 .

[37]  Allen M. Poteshman Underreaction, Overreaction, and Increasing Misreaction to Information in the Options Market , 2000 .

[38]  C. Gollier,et al.  Information and the Equity Premium , 2006 .

[39]  Hatem Ben-Ameur,et al.  A Stochastic Dynamic Program for Valuing Options on Futures , 2014 .

[40]  F. Rinaldi,et al.  Ambiguity in asset pricing and portfolio choice: a review of the literature , 2010 .

[41]  The Information Content of Implied Volatilities and Model-Free Volatility Expectations: Evidence from Options Written on Individual Stocks , 2007 .

[42]  David Kelsey,et al.  Asymmetric Momentum Effects Under Uncertainty , 2011 .

[43]  Ephraim Clark,et al.  Modelling credit spreads with time volatility, skewness, and kurtosis , 2015, Annals of Operations Research.

[44]  D. Roubaud,et al.  Real Options under Choquet-Brownian Ambiguity , 2010 .

[45]  Lars Peter Hansen,et al.  Robustness and US Monetary , 2008 .

[46]  José Heleno Faro,et al.  Pricing rules and Arrow–Debreu ambiguous valuation , 2010 .

[47]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[48]  D. Ghosh,et al.  Arbitrage, Hedging, and Speculation: The Foreign Exchange Market , 2004 .

[49]  Jun Pan,et al.  An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks , 2005 .

[50]  Hung T. Nguyen,et al.  On some claims related to Choquet integral risk measures , 2012, Ann. Oper. Res..

[51]  Andrea Buraschi,et al.  Differences in beliefs and currency risk premiums , 2010 .

[52]  David Feldman,et al.  Incomplete information equilibria: Separation theorems and other myths , 2007, Ann. Oper. Res..

[53]  Rudi Zagst,et al.  Stochastic dominance of portfolio insurance strategies , 2011, Ann. Oper. Res..

[54]  A. Chateauneuf,et al.  Choquet Pricing for Financial Markets with Frictions , 1996 .

[55]  P. Wakker,et al.  Nonmonotonic Choquet Integrals , 2001 .

[56]  I. Drechsler Uncertainty, Time-Varying Fear, and Asset Prices: Uncertainty, Time-Varying Fear, and Asset Prices , 2013 .

[57]  Sebastian Jaimungal,et al.  Incorporating Risk and Ambiguity Aversion into a Hybrid Model of Default , 2009 .

[58]  S. Muzzioli Option-based forecasts of volatility: an empirical study in the DAX-index options market , 2008 .

[59]  Alireza Arshadi Khamseh,et al.  Developing a multi-period robust optimization model considering American style options , 2015, Ann. Oper. Res..

[60]  F. Knight The economic nature of the firm: From Risk, Uncertainty, and Profit , 2009 .

[61]  E. Agliardi,et al.  The effects of environmental taxes and quotas on the optimal timing of emission reductions under Choquet-Brownian uncertainty , 2011 .

[62]  R. Whaley Understanding the VIX , 2009, The Journal of Portfolio Management.

[63]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[64]  David Schmeidleis SUBJECTIVE PROBABILITY AND EXPECTED UTILITY WITHOUT ADDITIVITY , 1989 .

[65]  Itzhak Gilboa,et al.  Additive representations of non-additive measures and the choquet integral , 1994, Ann. Oper. Res..

[66]  Rose-Anne Dana,et al.  On Equilibria when Agents Have Multiple Priors , 2002, Ann. Oper. Res..

[67]  Yuri Lawryshyn,et al.  A new rank dependent utility approach to model risk averse preferences in portfolio optimization , 2016, Ann. Oper. Res..

[68]  Aldo Montesano,et al.  Effects of Uncertainty Aversion on the Call Option Market , 2008 .

[69]  Eric Ghysels,et al.  The impact of risk and uncertainty on expected returns. , 2009 .

[70]  Lenos Trigeorgis,et al.  Choquet-based European option pricing with stochastic (and fixed) strikes , 2015, OR Spectr..

[71]  Joseph E. Stiglitz,et al.  RETHINKING MACROECONOMICS: WHAT FAILED, AND HOW TO REPAIR IT , 2011 .

[72]  N. Prabhala,et al.  The relation between implied and realized volatility , 1998 .

[73]  Kiyohiko G. Nishimura,et al.  Irreversible investment and Knightian uncertainty , 2002, J. Econ. Theory.

[74]  Constantin Mellios Interest rate options valuation under incomplete information , 2007, Ann. Oper. Res..

[75]  S. Heston A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[76]  R. Kast,et al.  Valuing future cash flows with non separable discount factors and non additive subjective measures: conditional Choquet capacities on time and on uncertainty , 2010 .

[77]  M. David HARRISON, J. Michael, and KREPS, . Martingales and Arbitrage in Multiperiod Securities Markets, Journal of Economic Theory, , . , 1979 .

[78]  A. Chateauneuf,et al.  Conditioning Capacities and Choquet Integrals: The Role of Comonotony , 2001 .

[79]  J. Keynes,et al.  The General Theory of Employment, Interest and Money. , 1936 .

[80]  F. Riedel Optimal Stopping With Multiple Priors , 2009 .

[81]  R. Thaler,et al.  Further Evidence On Investor Overreaction and Stock Market Seasonality , 1987 .

[82]  F. Trojani,et al.  Robustness and Ambiguity Aversion in General Equilibrium , 2004 .

[83]  Alain Chateauneuf,et al.  Choice under uncertainty with the best and worst in mind: Neo-additive capacities , 2007, J. Econ. Theory.