IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v70y2022i6p3108-3124.html
   My bibliography  Save this article

Dark Matter in (Volatility and) Equity Option Risk Premiums

Author

Listed:
  • Gurdip Bakshi

    (Fox School of Business, Temple University, Philadelphia, Pennsylvania 19122)

  • John Crosby

    (Strome College of Business, Old Dominion University, Norfolk, Virginia 23529)

  • Xiaohui Gao

    (Fox School of Business, Temple University, Philadelphia, Pennsylvania 19122)

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, 2022. "Dark Matter in (Volatility and) Equity Option Risk Premiums," Operations Research, INFORMS, vol. 70(6), pages 3108-3124, November.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:6:p:3108-3124
    DOI: 10.1287/opre.2022.2360
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2022.2360
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2022.2360?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Joshua D. Coval & Tyler Shumway, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, June.
    20. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Junyu & Ruan, Xinfeng, 2025. "Inferring jump dynamics from weekly options: A non-parametric method," Finance Research Letters, Elsevier, vol. 76(C).
    2. Stahl, Philip & Blauth, Jérôme, 2025. "Martingale defects in the volatility surface and bubble conditions in the underlying," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 154110, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Audrino, Francesco & Fengler, Matthias R., 2015. "Are classical option pricing models consistent with observed option second-order moments? Evidence from high-frequency data," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 46-63.
    2. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, University Library of Munich, Germany.
    3. Alexiou, Lykourgos & Rompolis, Leonidas S., 2024. "Jump tail risk exposure and the cross-section of stock returns," Journal of Empirical Finance, Elsevier, vol. 79(C).
    4. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    5. Mathieu Fournier & Kris Jacobs & Piotr Orłowski, 2024. "Modeling Conditional Factor Risk Premia Implied by Index Option Returns," Journal of Finance, American Finance Association, vol. 79(3), pages 2289-2338, June.
    6. Byun, Suk Joon & Jeon, Byoung Hyun & Min, Byungsun & Yoon, Sun-Joong, 2015. "The role of the variance premium in Jump-GARCH option pricing models," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 38-56.
    7. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2020. "A Theory of Equivalent Expectation Measures for Contingent Claim Returns," Papers 2006.15312, arXiv.org, revised May 2022.
    8. Du Du & Dan Luo, 2019. "The Pricing of Jump Propagation: Evidence from Spot and Options Markets," Management Science, INFORMS, vol. 67(5), pages 2360-2387, May.
    9. Mi‐Hsiu Chiang & Hsin‐Yu Chiu & Robin K. Chou, 2021. "Relevance of the disposition effect on the options market: New evidence," Financial Management, Financial Management Association International, vol. 50(1), pages 75-106, March.
    10. Jacobs, Kris & Li, Bingxin, 2023. "Option Returns, Risk Premiums, and Demand Pressure in Energy Markets," Journal of Banking & Finance, Elsevier, vol. 146(C).
    11. Nawalkha, Sanjay K & Zhuo, Xiaoyang, 2020. "A Theory of Equivalent Expectation Measures for Expected Prices of Contingent Claims," OSF Preprints hsxtu, Center for Open Science.
    12. Lu, Zhongjin & Murray, Scott, 2019. "Bear beta," Journal of Financial Economics, Elsevier, vol. 131(3), pages 736-760.
    13. Dario Alitab & Giacomo Bormetti & Fulvio Corsi & Adam A. Majewski, 2019. "A realized volatility approach to option pricing with continuous and jump variance components," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 639-664, December.
    14. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    15. Li, Minqiang, 2008. "Price Deviations of S&P 500 Index Options from the Black-Scholes Formula Follow a Simple Pattern," MPRA Paper 11530, University Library of Munich, Germany.
    16. Bondarenko, Oleg, 2014. "Variance trading and market price of variance risk," Journal of Econometrics, Elsevier, vol. 180(1), pages 81-97.
    17. Michael C. Fu & Bingqing Li & Rongwen Wu & Tianqi Zhang, 2020. "Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model," Papers 2006.15054, arXiv.org.
    18. David Volkmann, 2021. "Explaining S&P500 option returns: an implied risk-adjusted approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 665-685, June.
    19. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2020. "The Pricing of Tail Risk and the Equity Premium: Evidence From International Option Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 662-678, July.
    20. Shackleton, Mark B. & Voukelatos, Nikolaos, 2013. "Hedging efficiency in the Greek options market before and after the financial crisis of 2008," Journal of Multinational Financial Management, Elsevier, vol. 23(1), pages 1-18.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:70:y:2022:i:6:p:3108-3124. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.