Modeling Volatility Risk in Equity Options Market: A Statistical Approach

Abstract

This paper provides a cross-sectional analysis of U.S. option markets based on implied volatility data from August 2004 to August 2013. We analyse the implied volatility surface (IVS) for each security in the OptionMetrics database. We use implied volatility data across 13 deltas and 4 expiration dates. Employing methods from principal component analysis (PCA), and results from random matrix theory (RMT), we identify the signicant eigenvalues of the correlation matrix of implied volatilities and conclude that, usually, three principal components suce to reproduce the IVS. In this way we reduce dimensionality of the options market without loosing meaningful information. From this analysis we classify equities into those carrying mostly \systemic risk and into those carrying mostly \idiosyncratic risk. Based on the PCA results, we formulate a model which can be used to describe the dynamics of the joint statistics of the IVS of all U.S. options, yet is compact and computationally feasible. Using 9 volatility points to represents each IVS, the model oers signicant