IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

The Factor Structure in Equity Options

  • Peter Christoffersen

    ()

    (University of Toronto and CREATES)

  • Mathieu Fournier

    ()

    (Rotman School of Management)

  • Kris Jacobs

    ()

    (University of Houston)

Principal component analysis of equity options on Dow-Jones firms reveals a strong factor structure. The first principal component explains 77% of the variation in the equity volatility level, 77% of the variation in the equity option skew, and 60% of the implied volatility term structure across equities. Furthermore, the first principal component has a 92% correlation with S&P500 index option volatility, a 64% correlation with the index option skew, and a 80% correlation with the index option term structure. We develop an equity option valuation model that captures this factor structure. The model allows for stochastic volatility in the market return and also in the idiosyncratic part of firm returns. The model predicts that firms with higher betas have higher implied volatilities, and steeper moneyness and term structure slopes. We provide a tractable approach for estimating the model on a large set of index and equity option data on which the model provides a good fit. The equity option data support the cross-sectional implications of the estimated model.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: ftp://ftp.econ.au.dk/creates/rp/13/rp13_47.pdf
Download Restriction: no

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2013-47.

as
in new window

Length: 58
Date of creation: 06 2013
Date of revision:
Handle: RePEc:aah:create:2013-47
Contact details of provider: Web page: http://www.econ.au.dk/afn/

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Tim Bollerslev & Viktor Todorov, 2009. "Tails, Fears and Risk Premia," CREATES Research Papers 2009-26, School of Economics and Management, University of Aarhus.
  2. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  3. Jin-Chuan Duan & Jason Wei, 2009. "Systematic Risk and the Price Structure of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1981-2006, May.
  4. Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
  5. Peter Carr & Dilip Madan, 2012. "Factor Models for Option Pricing," Asia-Pacific Financial Markets, Springer, vol. 19(4), pages 319-329, November.
  6. Jérome Detemple & Marcel Rindisbacher, 2010. "Dynamic Asset Allocation: Portfolio Decomposition Formula and Applications," Review of Financial Studies, Society for Financial Studies, vol. 23(1), pages 25-100, January.
  7. George M. Constantinides & Michal Czerwonko & Jens Carsten Jackwerth & Stylianos Perrakis, 2010. "Are Options on Index Futures Profitable for Risk Averse Investors? Empirical Evidence," NBER Working Papers 16302, National Bureau of Economic Research, Inc.
  8. Adrian Buss & Grigory Vilkov, 2012. "Measuring Equity Risk with Option-implied Correlations," Review of Financial Studies, Society for Financial Studies, vol. 25(10), pages 3113-3140.
  9. Mo, Henry & Wu, Liuren, 2007. "International capital asset pricing: Evidence from options," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 465-498, September.
  10. Dennis, Patrick & Mayhew, Stewart, 2002. "Risk-Neutral Skewness: Evidence from Stock Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(03), pages 471-493, September.
  11. Goyal, Amit & Saretto, Alessio, 2009. "Cross-section of option returns and volatility," Journal of Financial Economics, Elsevier, vol. 94(2), pages 310-326, November.
  12. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  13. Broadie, Mark & Chernov, Mikhail & Johannes, Michael, 2007. "Understanding Index Option Returns," CEPR Discussion Papers 6239, C.E.P.R. Discussion Papers.
  14. Peter Carr & Liuren Wu, 2004. "Stochastic Skew in Currency Options," Finance 0409014, EconWPA.
  15. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
  16. Peter Reinhard Hansen & Asger Lunde & Valeri Voev, 2012. "Realized Beta GARCH: A Multivariate GARCH Model with Realized Measures of Volatility and Covolatility," Global COE Hi-Stat Discussion Paper Series gd12-269, Institute of Economic Research, Hitotsubashi University.
  17. Bates, David S., 2008. "The market for crash risk," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2291-2321, July.
  18. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA.
  19. 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.
  20. 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.
  21. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
  22. Joost Driessen & Pascal J. Maenhout & Grigory Vilkov, 2009. "The Price of Correlation Risk: Evidence from Equity Options," Journal of Finance, American Finance Association, vol. 64(3), pages 1377-1406, 06.
  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. Bo-Young Chang & Peter Christoffersen & Kris Jacobs & Gregory Vainberg, 2009. "Option-Implied Measures of Equity Risk," CIRANO Working Papers 2009s-33, CIRANO.
  25. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
  26. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, 06.
  27. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:aah:create:2013-47. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.