The Relationship between the Volatility of Returns and the Number of Jumps in Financial Markets

We propose a methodology to employ high frequency financial data to obtain estimates of volatility of log-prices which are not affected by microstructure noise and Lévy jumps. We introduce the 'number of jumps' as a variable to explain and predict volatility and show that the number of jumps in SPY prices is an important variable to explain the daily volatility of the SPY log-returns, has more explanatory power than other variables (e.g. high and low, open and close), and has a similar explanatory power to that of the VIX. Finally, number of jumps is very useful to forecast volatility and contains information that is not impounded in the VIX