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.