IDEAS home Printed from https://ideas.repec.org/a/taf/jnlbes/v38y2020i3p662-678.html
   My bibliography  Save this article

The Pricing of Tail Risk and the Equity Premium: Evidence From International Option Markets

Author

Listed:
  • Torben G. Andersen
  • Nicola Fusari
  • Viktor Todorov

Abstract

We explore the pricing of tail risk as manifest in index options across international equity markets. The risk premium associated with negative tail events displays persistent shifts, unrelated to volatility. This tail risk premium is a potent predictor of future returns for all the indices, while the option-implied volatility only forecasts the future return variation. Hence, compensation for negative jump risk is the primary driver of the equity premium, whereas the reward for pure diffusive variance risk is unrelated to future equity returns. We also document pronounced commonalities, suggesting a high degree of integration among the major global equity markets. KEY WORDS: Equity risk premium; International option markets; Predictability; Tail risk; Variance risk premium.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlbes:v:38:y:2020:i:3:p:662-678
    DOI: 10.1080/07350015.2018.1564318
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07350015.2018.1564318
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07350015.2018.1564318?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
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    3. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    4. 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.
    5. Bollerslev, Tim & Marrone, James & Xu, Lai & Zhou, Hao, 2014. "Stock Return Predictability and Variance Risk Premia: Statistical Inference and International Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(3), pages 633-661, June.
    6. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat, 2012. "Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options," Journal of Financial Economics, Elsevier, vol. 106(3), pages 447-472.
    7. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    8. Petar Sabtchevsky & Paul Whelan & Andrea Vedolin & Philippe Mueller, 2017. "Variance Risk Premia on Stocks and Bonds," 2017 Meeting Papers 1161, Society for Economic Dynamics.
    9. Campbell, John Y & Hamao, Yasushi, 1992. "Predictable Stock Returns in the United States and Japan: A Study of Long-Term Capital Market Integration," Journal of Finance, American Finance Association, vol. 47(1), pages 43-69, March.
    10. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    11. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
    12. Bekaert, Geert & Hodrick, Robert J, 1992. "Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets," Journal of Finance, American Finance Association, vol. 47(2), pages 467-509, June.
    13. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    14. Londono, Juan M. & Zhou, Hao, 2017. "Variance risk premiums and the forward premium puzzle," Journal of Financial Economics, Elsevier, vol. 124(2), pages 415-440.
    15. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    16. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
    17. 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.
    18. Hjalmarsson, Erik, 2010. "Predicting Global Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(1), pages 49-80, February.
    19. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    20. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    21. Junye Li & Gabriele Zinna, 2018. "The Variance Risk Premium: Components, Term Structures, and Stock Return Predictability," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 411-425, July.
    22. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    23. Pedro Santa-Clara & Shu Yan, 2010. "Crashes, Volatility, and the Equity Premium: Lessons from S&P 500 Options," The Review of Economics and Statistics, MIT Press, vol. 92(2), pages 435-451, May.
    24. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    25. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    26. Peter C. B. Phillips, 2014. "On Confidence Intervals for Autoregressive Roots and Predictive Regression," Econometrica, Econometric Society, vol. 82(3), pages 1177-1195, May.
    27. Torben G. Andersen & Oleg Bondarenko & Maria T. Gonzalez-Perez, 2015. "Exploring Return Dynamics via Corridor Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 28(10), pages 2902-2945.
    28. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
    29. Harvey, Campbell R, 1991. "The World Price of Covariance Risk," Journal of Finance, American Finance Association, vol. 46(1), pages 111-157, March.
    30. Bakshi, Gurdip & Panayotov, George & Skoulakis, Georgios, 2011. "Improving the predictability of real economic activity and asset returns with forward variances inferred from option portfolios," Journal of Financial Economics, Elsevier, vol. 100(3), pages 475-495, June.
    31. Wang, Hao & Zhou, Hao & Zhou, Yi, 2013. "Credit default swap spreads and variance risk premia," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3733-3746.
    32. Ferson, Wayne E & Harvey, Campbell R, 1993. "The Risk and Predictability of International Equity Returns," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 527-566.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Mete Kilic & Ivan Shaliastovich, 2019. "Good and Bad Variance Premia and Expected Returns," Management Science, INFORMS, vol. 67(6), pages 2522-2544, June.
    3. Pyun, Sungjune, 2019. "Variance risk in aggregate stock returns and time-varying return predictability," Journal of Financial Economics, Elsevier, vol. 132(1), pages 150-174.
    4. Diego Amaya & Jean-François Bégin & Geneviève Gauthier, 2022. "The Informational Content of High-Frequency Option Prices," Management Science, INFORMS, vol. 68(3), pages 2166-2201, March.
    5. 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.
    6. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2018. "Model Complexity and Out-of-Sample Performance: Evidence from S&P 500 Index Returns," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 1-29.
    7. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2017. "Short-Term Market Risks Implied by Weekly Options," Journal of Finance, American Finance Association, vol. 72(3), pages 1335-1386, June.
    8. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    9. Li, Zhenxiong & Yao, Xingzhi & Izzeldin, Marwan, 2023. "On the right jump tail inferred from the VIX market," International Review of Financial Analysis, Elsevier, vol. 86(C).
    10. Hsuan‐Ling Chang & Yen‐Cheng Chang & Hung‐Wen Cheng & Po‐Hsiang Peng & Kevin Tseng, 2019. "Jump variance risk: Evidence from option valuation and stock returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(7), pages 890-915, July.
    11. Andersen, Torben G. & Todorov, Viktor & Ubukata, Masato, 2021. "Tail risk and return predictability for the Japanese equity market," Journal of Econometrics, Elsevier, vol. 222(1), pages 344-363.
    12. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    13. Yabei Zhu & Xingguo Luo & Qi Xu, 2023. "Industry variance risk premium, cross‐industry correlation, and expected returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(1), pages 3-32, January.
    14. Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S. & Grose, Simone D., 2012. "Probabilistic forecasts of volatility and its risk premia," Journal of Econometrics, Elsevier, vol. 171(2), pages 217-236.
    15. 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.
    16. Eric Jacquier & Cedric Okou, 2013. "Disentangling Continuous Volatility from Jumps in Long-Run Risk-Return Relationships," CIRANO Working Papers 2013s-14, CIRANO.
    17. Peter F. Christoffersen & Francis X. Diebold, 2006. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," Management Science, INFORMS, vol. 52(8), pages 1273-1287, August.
    18. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    19. Junyu Zhang & Xinfeng Ruan & Jin E. Zhang, 2023. "Risk‐neutral moments and return predictability: International evidence," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(5), pages 1086-1111, August.
    20. Sévi, Benoît, 2013. "An empirical analysis of the downside risk-return trade-off at daily frequency," Economic Modelling, Elsevier, vol. 31(C), pages 189-197.

    More about this item

    Keywords

    equity risk premium; international option markets; predictability; tail risk; variance risk premium.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    Statistics

    Access and download statistics

    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:taf:jnlbes:v:38:y:2020:i:3:p:662-678. 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 Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UBES20 .

    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.