| This thesis provides a cross-sectional classification of optionable equities in U.S. Markets based on implied volatility data. For each security in the OptionMetrics database for which there is data available over the period from August 2004 to August 2013 we model its implied volatility surface (IVS). We then use the spectrum of the IVS, in particular the leading eigenvalue, to characterize options into those carrying mostly systemic risk and into those carrying mostly idiosyncratic risk. All available data from OptionMetrics results in a database of roughly 50 GB. We use implied volatility data across 13 different deltas and 4 expiration dates, hence our data on the options market is 52 times bigger than that of the equities market. By employing methods from principal component analysis (PCA) and results from random matrix theory (RMT), we classify the significant eigenvalues and conclude that usually three principal components suffice to reproduce the IVS. In this way we reduce dimensionality without loosing any meaningful information. Using these results, we formulate an explicit model which can be used to model the dynamics of the IVS, yet is compact and computationally feasible. Out of the original 52 implied volatility pivots we narrow our model to use only 6-pivots, offering roughly 9 times variable reduction. We backtest this model on different portfolios of options. Our model can be further used as a risk management system for option portfolios. |
