With the availability of high-frequency data, it is now possible to measure volatility in different time scales (from intraday to years); this has led to two interesting areas of research:
- High-frequency volatility: How does the discretization of prices (the tick size) changes the dynamics of the observed price and its relationship with the underlying price process? A simple and accurate model was introduced by Mathieu Rosenbaum in A new approach for the dynamics of ultra high frequency data: the model with uncertainty zones. In Microstructure Of A Central Limit Order Book In FX Futures, Marcos Carreira shows how different microstructure parameters can lead to very different statistics given the same price process.
- Rough volatility: In the seminal Volatility is rough paper, Mathieu Rosenbaum and his coauthors show that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale, and that long memory in volatility might be an artifact from the aplication of classical statistical procedures to assets that follow the rough fractional stochastic volatility (RFSV) model.