May’s Frontiers in Quantitative Finance webcast, co-sponsored by Mosaic Smart Data, was led by Dr Brian Healy from Decision Science Ltd and Professor Andrew Papanicolaou from New York University, who gave a joint presentation on Principal Component Analysis (PCA) of Implied Volatility Surfaces.
The presentation was based on new research carried out in collaboration with Professor Marco Avellaneda from New York University and Professor George Papanicolaou from Stanford University.
As an introduction to the subject, Dr Healy began by explaining how they applied PCA to U.S. equities’ returns. He discussed issues such as how many components should be removed for the residuals to be random, how to construct the explanatory factors and the natural structure of the data. He then demonstrated this by applying some results from random matrix theory to the data.
Professor Andrew Papanicolaou followed by discussing the application of PCA using tensors to implied volatility surface data, which is a higher-dimensional problem. When performing matrix PCA on the volatility surface data, they concluded that the number of significant components is 9. As a result of the structure contained in option prices, this is lower than is typical for equity returns, where the number is usually 20.
In a similar approach to a market capitalisation weighted equity factor or index, Healy and Papanicolaou used the open interest on the option and its vega to create a portfolio of implied volatility returns that tracks the volatility surface ‘EigenPortfolio’ – suggesting this can be used in similar ways to the VIX, the S&P 500 volatility index.
Healy and Papanicolaou concluded the talk by explaining how retaining the tensor structure in the ‘EigenPortfolio’ improves how well it tracks the open interest weighted implied volatility returns portfolio.
The online event was hosted by the Oxford Mathematical and Computational Finance Group and was attended by more than 130 participants from around the world. Follow Mosaic Smart Data on LinkedIn to ensure you don’t miss information on the next Group meeting which will be in June.