Price and Volatility Co-Jumps

Abstract

The dependence between the magnitudes of discontinuous changes in asset prices and contemporaneous discontinuous changes in volatility (co-jumps) is a fundamental aspect of the price process contributing, among other effects, to skewness in the return distribution. Yet, its nature has been reported by many as being - in terms of sign, magnitude, and statistical significance - largely elusive. Using a novel identification strategy for stochastic volatility modelling in continuous time relying on trade-level information for spot variance estimation, as well as infinitesimal cross-moments, this paper documents that a sizeable proportion of discontinuous changes in asset prices are associated with strongly anti-correlated, contemporaneous changes in volatility. Not only are the price jump sizes strongly negatively correlated with the volatility jump sizes, but the absolute values of their (negative) mean and dispersion appear to increase with the volatility level, an additional effect which should lead to care in the management of joint directional and volatility jump risk. Using a possibly non-monotonic pricing kernel, we illustrate the equilibrium impact of price and volatility co-jumps on both return and variance risk premia.

Keywords: Stochastic volatility, jumps in prices, jumps in volatility, co-jumps, infinitesimal cross-moments, return risk premia, variance risk premia