Assessing models of individual equity option prices

Abstract

This article investigates option models in the encompassing class of stochastic volatility, return-jumps, and volatility-jumps. Relying on individual equity options on the 50 most active firms and maximum likelihood estimation method, we obtain several findings. First, while stochastic volatility is as important for individual equity options as it is for index options, return-jumps and volatility-jumps are also essential in pricing individual equity options. Second, the double-jump model improves pricing performance beyond return-jumps absent volatility-jumps, and beyond volatility-jumps absent return-jumps. Third, between return-jumps and volatility-jumps, the former is empirically more relevant than the latter for pricing options; and fourth, the inverse link between volatility-jumps and return-jumps is instrumental for explaining the valuation of deep out-of-money puts and the option dynamics of firms with high kurtosis.