Jumps and Diffusive Variance: A Granular Analysis of Individual Stock Returns

Abstract

Jumps and diffusive changes in stock prices are different ways in which information is reflected in the prices. We use nonparametric methods to decompose returns on individual stocks into jumps and diffusive components. Contrary to the conventional assumption that jump intensity is positively related to diffusive variance, we find abundant evidence that realized jump intensity and diffusive variance are uncorrelated or negatively related for a majority of stocks. The jump-diffusion beta is found to positively contribute to the implied volatility smile of options on individual stocks. We also document a counter-cyclical pattern of realized jump sizes, which challenges the i.i.d. jump size assumption commonly seen in the literature. The findings provide useful guidance on modeling option prices.