PCA for Implied Volatility Surfaces

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.