The evolution of the Volatility in Financial Returns: Realized Volatility vs Stochastic Volatility Measures

In this paper, we calculate the realized volatility measures using intraday data not equally spaced in time. The aim is to compare these measures with the ones from the stochastic volatility model. With this model, the data used are obtained in equal time intervals. Known facts are that the volatility is not directly observable and time-varying. If we consider the set of the most flexible models to capture the volatility evolution of returns, the stochastic volatility model belongs to the aforementioned set. High-frequency observations are used, which means daily observations obtained in equal time intervals. Can this be compatible with ultra-high-frequency data and realized volatility measures? Can we obtain compatible measures of volatility with both approaches? This is the object of this paper.