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Dark Matter in (Volatility and) Equity Option Risk Premiums

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  • Gurdip Bakshi
  • John Crosby
  • Xiaohui Gao

Abstract

Emphasizing the statistics of jumps crossing the strike and local time, we develop a decomposition of equity option risk premiums. Operationalizing this theoretical treatment, we equip the pricing kernel process with unspanned risks, embed (unspanned) jump risks, and allow equity return volatility to contain unspanned risks. Unspanned risks are consistent with negative risk premiums for jumps crossing the strike and local time and imply negative risk premiums for out-of-the-money call options and straddles. The empirical evidence from weekly and farther-dated index options is supportive of our theory of economically relevant unspanned risks and reveals ``dark matter" in option risk premiums.

Suggested Citation

  • Gurdip Bakshi & John Crosby & Xiaohui Gao, 2023. "Dark Matter in (Volatility and) Equity Option Risk Premiums," Papers 2303.16371, arXiv.org.
  • Handle: RePEc:arx:papers:2303.16371
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    1. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    2. Peter Christoffersen & Steven Heston & Kris Jacobs, 2013. "Capturing Option Anomalies with a Variance-Dependent Pricing Kernel," The Review of Financial Studies, Society for Financial Studies, vol. 26(8), pages 1963-2006.
    3. Ning Cai & S. G. Kou, 2011. "Option Pricing Under a Mixed-Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 57(11), pages 2067-2081, November.
    4. Yacine Aït-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-1050, December.
    5. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    6. Peter Christoffersen & Ruslan Goyenko & Kris Jacobs & Mehdi Karoui, 2018. "Illiquidity Premia in the Equity Options Market," The Review of Financial Studies, Society for Financial Studies, vol. 31(3), pages 811-851.
    7. Andersen, Torben G. & Fusari, Nicola & Todorov, Viktor, 2015. "The risk premia embedded in index options," Journal of Financial Economics, Elsevier, vol. 117(3), pages 558-584.
    8. Joshua D. Coval & Tyler Shumway, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, June.
    9. Peter Carr & Liuren Wu, 2003. "What Type of Process Underlies Options? A Simple Robust Test," Journal of Finance, American Finance Association, vol. 58(6), pages 2581-2610, December.
    10. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    11. Xu Cheng & Winston Wei Dou & Zhipeng Liao, 2022. "Macro‐Finance Decoupling: Robust Evaluations of Macro Asset Pricing Models," Econometrica, Econometric Society, vol. 90(2), pages 685-713, March.
    12. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    13. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    14. Christopher S. Jones, 2006. "A Nonlinear Factor Analysis of S&P 500 Index Option Returns," Journal of Finance, American Finance Association, vol. 61(5), pages 2325-2363, October.
    15. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    16. Dmitriy Muravyev & Neil D Pearson & Stijn Van Nieuwerburgh, 2020. "Options Trading Costs Are Lower than You Think," The Review of Financial Studies, Society for Financial Studies, vol. 33(11), pages 4973-5014.
    17. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    18. Mark Broadie & Mikhail Chernov & Michael Johannes, 2009. "Understanding Index Option Returns," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4493-4529, November.
    19. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    20. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    21. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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