Abstract
This paper evaluates the forecasting performance of a Brownian semi-stationary (BSS) process in modelling the volatility of 21 equity indices. We implement a hybrid scheme to simulate BSS processes with high efficiency and precision. These simulations are useful to price derivatives, accounting for rough volatility. We then calibrate the BSS parameters for the realised kernel of 21 equity indices, using data from the Oxford-Man Institute. Finally, we conduct one-step and ten-step ahead forecasts on six indices and find that the BSS outperforms benchmarks, including a Log-HAR specification, in most cases.
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