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The risk premium that never was: A fair value explanation of the volatility spread

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  • McGee, Richard J.
  • McGroarty, Frank

Abstract

We present a new framework to investigate the profitability of trading the volatility spread, the upward bias on implied volatility as an estimator of future realized volatility. The scheme incorporates the first four option-implied moments in a growth-optimal payoff that is statically replicated using a portfolio of options. Removing the upward bias on implied volatility worsens the likelihood score of risk-neutral densities obtained from S&P 500 index options when they are used as forecasts of the underlying index return distribution. It also results in negative expected capital growth when they are used in a volatility arbitrage scheme. Our empirical finding is that the upward bias on implied volatility does not represent a long-term return premium, rather it is required to mitigate the large losses associated with tail events when trading volatility in options markets.

Suggested Citation

  • McGee, Richard J. & McGroarty, Frank, 2017. "The risk premium that never was: A fair value explanation of the volatility spread," European Journal of Operational Research, Elsevier, vol. 262(1), pages 370-380.
    • Handle: RePEc:eee:ejores:v:262:y:2017:i:1:p:370-380
    DOI: 10.1016/j.ejor.2017.03.070
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    as
    1. David Edelman, 2000. "On the Financial Value of Information," Annals of Operations Research, Springer, vol. 100(1), pages 123-132, December.
    2. Bekaert, Geert & Hoerova, Marie & Lo Duca, Marco, 2013. "Risk, uncertainty and monetary policy," Journal of Monetary Economics, Elsevier, vol. 60(7), pages 771-788.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. D. J. Johnstone, 2011. "Economic Interpretation of Probabilities Estimated by Maximum Likelihood or Score," Management Science, INFORMS, vol. 57(2), pages 308-314, February.
    5. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    6. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    7. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    8. Peter H. GRUBER & Claudio TEBALDI & Fabio TROJANI, 2015. "The Price of the Smile and Variance Risk Premia," Swiss Finance Institute Research Paper Series 15-36, Swiss Finance Institute.
    9. George J. Jiang & Yisong S. Tian, 2005. "The Model-Free Implied Volatility and Its Information Content," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1305-1342.
    10. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
    11. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," European Journal of Operational Research, Elsevier, vol. 251(1), pages 124-134.
    12. Kyle Jurado & Sydney C. Ludvigson & Serena Ng, 2015. "Measuring Uncertainty," American Economic Review, American Economic Association, vol. 105(3), pages 1177-1216, March.
    13. Francis A. Longstaff & Jun Pan & Lasse H. Pedersen & Kenneth J. Singleton, 2011. "How Sovereign Is Sovereign Credit Risk?," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(2), pages 75-103, April.
    14. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, May.
    15. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-681.
    16. Fabozzi, Frank J. & Paletta, Tommaso & Stanescu, Silvia & Tunaru, Radu, 2016. "An improved method for pricing and hedging long dated American options," European Journal of Operational Research, Elsevier, vol. 254(2), pages 656-666.
    17. Turan G. Bali & Armen Hovakimian, 2009. "Volatility Spreads and Expected Stock Returns," Management Science, INFORMS, vol. 55(11), pages 1797-1812, November.
    18. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    19. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
    20. Gurdip Bakshi & Dilip Madan, 2006. "A Theory of Volatility Spreads," Management Science, INFORMS, vol. 52(12), pages 1945-1956, December.
    21. Bao, Qunfang & Li, Shenghong & Gong, Donggeng, 2012. "Pricing VXX option with default risk and positive volatility skew," European Journal of Operational Research, Elsevier, vol. 223(1), pages 246-255.
    22. Yoshida, Yuji, 2003. "The valuation of European options in uncertain environment," European Journal of Operational Research, Elsevier, vol. 145(1), pages 221-229, February.
    23. Jorion, Philippe, 1995. "Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-528, June.
    24. Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," The Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
    25. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    26. Itamar Drechsler, 2013. "Uncertainty, Time-Varying Fear, and Asset Prices," Journal of Finance, American Finance Association, vol. 68(5), pages 1843-1889, October.
    27. Date, Paresh & Islyaev, Suren, 2015. "A fast calibrating volatility model for option pricing," European Journal of Operational Research, Elsevier, vol. 243(2), pages 599-606.
    28. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.
    29. Eric Ghysels & Fangfang Wang, 2014. "Moment-Implied Densities: Properties and Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 88-111, January.
    30. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
    31. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
    32. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    33. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
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    2. Fabian Hollstein & Marcel Prokopczuk & Björn Tharann & Chardin Wese Simen, 2019. "Predicting the equity market with option-implied variables," The European Journal of Finance, Taylor & Francis Journals, vol. 25(10), pages 937-965, July.
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