Testing and forecasting price jumps with return moments

Abstract

We detect jumps with the cubic variation and derive its exact distribution under a generic pure-diffusion model with deterministic time-varying volatility. Our method performs well for not only high- but also low-frequency returns. We use the jump testing method to construct monthly and daily jump indicators from the daily and intraday S&P 500 index returns, and find that they can be significantly and robustly predicted by VIX. Other option-implied and historical moments are either subsumed by VIX or are conditionally useful. Our results support the superior informational role played by the risk-neutral volatility in predicting future price jump events.