IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2002.00085.html
   My bibliography  Save this paper

PCA for Implied Volatility Surfaces

Author

Listed:
  • Marco Avellaneda
  • Brian Healy
  • Andrew Papanicolaou
  • George Papanicolaou

Abstract

Principal component analysis (PCA) is a useful tool when trying to construct factor models from historical asset returns. For the implied volatilities of U.S. equities there is a PCA-based model with a principal eigenportfolio whose return time series lies close to that of an overarching market factor. The authors show that this market factor is the index resulting from the daily compounding of a weighted average of implied-volatility returns, with weights based on the options' open interest (OI) and Vega. The authors also analyze the singular vectors derived from the tensor structure of the implied volatilities of S&P500 constituents, and find evidence indicating that some type of OI and Vega-weighted index should be one of at least two significant factors in this market.

Suggested Citation

  • Marco Avellaneda & Brian Healy & Andrew Papanicolaou & George Papanicolaou, 2020. "PCA for Implied Volatility Surfaces," Papers 2002.00085, arXiv.org.
    • Handle: RePEc:arx:papers:2002.00085
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2002.00085
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    3. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    4. Phelim Boyle, 2014. "Positive Weights on the Efficient Frontier," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(4), pages 462-477, October.
    5. Marco Avellaneda, 2019. "Hierarchical PCA and Applications to Portfolio Management," Papers 1910.02310, arXiv.org.
    6. Roll, Richard & Ross, Stephen A, 1980. "An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
    7. Marco Avellaneda & Jeong-Hyun Lee, 2010. "Statistical arbitrage in the US equities market," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 761-782.
    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. Jan Rosenzweig, 2020. "Fat Tailed Factors," Papers 2011.13637, arXiv.org, revised Dec 2021.
    2. Choi, Jungjun & Yang, Xiye, 2022. "Asymptotic properties of correlation-based principal component analysis," Journal of Econometrics, Elsevier, vol. 229(1), pages 1-18.
    3. Rama Cont, 2023. "In memoriam: Marco Avellaneda (1955–2022)," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 3-15, January.

    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. Marco Avellaneda & Juan Andr'es Serur, 2020. "Hierarchical PCA and Modeling Asset Correlations," Papers 2010.04140, arXiv.org.
    2. Firoozye, Nikan & Tan, Vincent & Zohren, Stefan, 2023. "Canonical portfolios: Optimal asset and signal combination," Journal of Banking & Finance, Elsevier, vol. 154(C).
    3. Daniel Bartz & Kerr Hatrick & Christian W Hesse & Klaus-Robert Müller & Steven Lemm, 2013. "Directional Variance Adjustment: Bias Reduction in Covariance Matrices Based on Factor Analysis with an Application to Portfolio Optimization," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
    4. Lars Hornuf & Paul P. Momtaz & Rachel J. Nam & Ye Yuan, 2023. "Cybercrime on the Ethereum Blockchain," CESifo Working Paper Series 10598, CESifo.
    5. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    6. Thomas W. Downs & Robert W. Ingram, 2000. "Beta, Size, Risk, And Return," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 23(3), pages 245-260, September.
    7. Paul Munene Muiruri, 2014. "Effects of Estimating Systematic Risk in Equity Stocks in the Nairobi Securities Exchange (NSE) (An Empirical Review of Systematic Risks Estimation)," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 4(4), pages 228-248, October.
    8. Attiya Yasmeen Javid, 2000. "Alternative Capital Asset Pricing Models: A Review of Theory and Evidence," PIDE Research Report 2000:3, Pakistan Institute of Development Economics.
    9. Mahsa Ghorbani & Edwin K. P. Chong, 2018. "Stock Price Prediction using Principle Components," Papers 1803.05075, arXiv.org.
    10. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    11. Deshen Wang, 2017. "Adjustable Robust Singular Value Decomposition: Design, Analysis and Application to Finance," Data, MDPI, vol. 2(3), pages 1-15, August.
    12. Trabelsi, Mohamed Ali, 2010. "Choix de portefeuille: comparaison des différentes stratégies [Portfolio selection: comparison of different strategies]," MPRA Paper 82946, University Library of Munich, Germany, revised 01 Dec 2010.
    13. Miras, Hassan & Masih, Mansur, 2017. "Stock returns and macroeconomic factors in an emerging economy: Malaysian evidence," MPRA Paper 101229, University Library of Munich, Germany.
    14. Park, Byeong U. & Mammen, Enno & Härdle, Wolfgang & Borak, Szymon, 2009. "Time Series Modelling With Semiparametric Factor Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 284-298.
    15. Panigirtzoglou, Nikolaos & Skiadopoulos, George, 2004. "A new approach to modeling the dynamics of implied distributions: Theory and evidence from the S&P 500 options," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1499-1520, July.
    16. Zura Kakushadze & Willie Yu, 2016. "Multifactor Risk Models and Heterotic CAPM," Papers 1602.04902, arXiv.org, revised Mar 2016.
    17. Samih Antoine Azar, 2013. "The Spurious Relation between Inflation Uncertainty and Stock Returns: Evidence from the U.S," Review of Economics & Finance, Better Advances Press, Canada, vol. 3, pages 99-109, November.
    18. Hengxu Lin & Dong Zhou & Weiqing Liu & Jiang Bian, 2021. "Deep Risk Model: A Deep Learning Solution for Mining Latent Risk Factors to Improve Covariance Matrix Estimation," Papers 2107.05201, arXiv.org, revised Oct 2021.
    19. Xia, Hui & Min, Xinyu & Deng, Shijie, 2015. "Effectiveness of earnings forecasts in efficient global portfolio construction," International Journal of Forecasting, Elsevier, vol. 31(2), pages 568-574.
    20. Xi Luo, 2011. "Recovering Model Structures from Large Low Rank and Sparse Covariance Matrix Estimation," Papers 1111.1133, arXiv.org, revised Mar 2013.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2002.00085. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.