The Role of Price‐Volatility Cojumps in Volatility Forecasting

ABSTRACT This paper investigates whether simultaneous jumps in prices and volatility improve volatility forecasting. Using up‐to‐date high‐frequency S&P 500 and VIX data, we identify price‐volatility cojumps at the intraday granularity and construct upside, downside, and asymmetric measures. Embedding these into the Heterogeneous Autoregressive (HAR) model, we provide new empirical evidence that downside cojumps increase future volatility, upside cojumps reduce volatility. Out‐of‐sample analysis further shows that incorporating these impacts of cojumps significantly enhances HAR model forecasting performance. Moreover, our results reveal that recent price jumps become important predictors of volatility when accompanied by simultaneous volatility jumps, an effect not previously documented in the literature. Finally, we also document the economic interpretation, policy implications, and economic value of price‐volatility cojumps.