Merton (1976) implied jump

Motivated by the widespread use of implied volatility in the Black-Scholes-Merton (BSM) model, we shift the concept to implied jumps using the Merton jump-diffusion (MJD) model, aiming to extract jump-related information in an analogous manner. Such a novel attempt introduces challenges in the estimation process, and thus, we propose a hybrid estimation procedure that incorporates a pre-search step to identify reliable initial values for the model parameters, thereby enhancing estimation accuracy. Using the daily cross-section of option prices, we construct two new indices: the Implied Jump Expectation Index (JIX) and the Jump Volatility Index (JVIX) to represent implied jump. Our empirical results indicate the implied jump combined with the implied diffusive risk under the MJD model significantly provides incremental predictive power for shortly future realized volatility compared with VIX9D and the historical components of HAR models. Also, we document that JIX has significantly predictive power for the next-day market return even under the market extreme events or high economic uncertainty.