Extended stochastic volatility models incorporating realised measures

Extended stochastic volatility models are studied which use the daily returns as well as the volatility information in intraday price data summarised in terms of a number of realised measures. These extended models treat the logarithm of daily volatility as a latent process with autoregressive structure, relate to daily returns via their variance models and relate to the logarithms of the realised measures via linear models. Fitting such an extended stochastic volatility model automatically combines the realised measures and daily returns into an overall daily volatility estimator. This process is technically rather demanding: Kalman filter and efficient importance sampling approaches are used here. The extended models are illustrated empirically using both high and low trading rate data. Simulation studies are reported which confirm that the model delivers volatility estimates that have better mean squared error and bias performance than individual realised measures.