On the relationship between conditional jump intensity and diffusive volatility

In standard options pricing models that include jump components to capture large price changes, the conditional jump intensity is typically specified as an increasing function of the diffusive volatility. We conduct model-free estimation and tests of the relationship between jump intensity and diffusive volatility. Simulation analysis confirms that the tests have power to reject the null hypothesis of no relationship if data are generated with the relationship. Applying the method to a few stock indexes and individual stocks, however, we find little evidence that jump intensity positively depends on diffusive volatility as a general property of the jump intensity. The findings of the paper give impetus to improving the specification of jump dynamics in options pricing models.