Understanding Equity Option Prices

Abstract

Principal component analysis of equity options on Dow-Jones …rms reveals a strong factor structure. The …rst principal component explains 66% of the variation in equity volatility level, 65% of the variation in the equity option skew and 61% of the implied volatility term structure across equities. Furthermore, the …rst principal component has an 88% correlation with S&P500 index option volatility, an 83% correlation with the index option skew, and a 66% correlation with the index option term structure. Based on these …ndings we develop an equity option valuation model that captures the cross-sectional market factor structure as well as stochastic volatility through time. The model assumes a Heston (1993) style stochastic volatility model for the market return but additionally allows for stochastic idiosyncratic volatility for each …rm. The model delivers theoretical predictions consistent with the empirical …ndings in Duan and Wei (2009). We provide a tractable approach for estimating the model on index and equity option data. The model provides a good …t to a large panel of options on stocks in the Dow-Jones index.