Combining sharp and smooth transitions in volatility dynamics: a fuzzy regime approach

Volatility in financial markets is characterized by alternating persistent turmoil and quiet periods, but also by a slowly–varying average level. This slow moving component keeps open the question of whether some of its features are better represented as abrupt or smooth changes between local averages of volatility. We provide a new class of models with a set of parameters subject to abrupt changes in regime (Markov Switching – MS) and another set subject to smooth transition (ST) changes. These models capture the possibility that regimes may overlap with one another (fuzzy). The empirical application is carried out on the volatility of four US indices. It shows that the flexibility of the new model allows for a better overall performance over either MS or ST, and provides a Local Average Volatility measure as a parametric estimation of the low frequency component.