PCA for Implied Volatility Surfaces

Marco Avellaneda, Brian Healy, Andrew Papanicolaou, George Papanicolaou

Research output: Contribution to journalArticlepeer-review


Principal component analysis (PCA) is a useful tool when trying to construct factor models from historical asset returns. For the implied volatilities of US equities, there is a PCA-based model with a principal eigenport-folio 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 and Vega. The authors also analyze the singular vectors derived from the tensor structure of the implied volatilities of S&P 500 constituents and find evidence indicating that some type of open interest-and Vega-weighted index should be one of at least two significant factors in this market.

Original languageEnglish (US)
Pages (from-to)85-109
Number of pages25
JournalJournal of Financial Data Science
Issue number2
StatePublished - Mar 1 2020


  • Big data/machine learning
  • Simulations
  • Statistical methods

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Information Systems
  • Finance
  • Business and International Management
  • Strategy and Management
  • Business, Management and Accounting (miscellaneous)
  • Information Systems and Management


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