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PCA for Implied Volatility Surfaces

Author

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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