Deducing the Implications of Jump Models for the Structure of Stock Market Crashes, Rallies, Jump Arrival Rates, and Extremes

This paper studies the structure of stock market crashes, rallies, their jump arrival rates, and extremes. Large market moves are characterized in a pure-jump modeling framework. Based on both raw and devolatized returns, it is shown empirically that crashes are more severe in intensity than rallies, and have higher arrival rates. At the same time, both left-tail and right-tail extreme events conform with Frechet limit laws. Pure-jump models which describe well the tail properties of market returns are identified via their Levy measures. The distribution of extreme events implied by our model's Levy measure is closer to the actual realization of extremes than those of competing models. Finally, there is information content in the Levy measure of pure-jump models for forward arrival rate of jumps