"Measuring and forecasting financial variability using realised variance with
and without a model"
Ole E. Barndorff-Nielsen
The Centre for Mathematical Physics and Stochastics (MaPhySto),
University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark.
Bent Nielsen
Nuffield College, University of Oxford, Oxford OX1 1NF, U.K.
Neil Shephard
Nuffield College, University of Oxford, Oxford OX1 1NF, U.K.
Carla Ysusi
Department of Statistics, University of Oxford,
South Parks Road, Oxford OX1 3TG, U.K.
We use high frequency financial data to proxy, via the realised variance,
each day's financial variability. Based on a semiparametric stochastic
volatility process, a limit theory shows you can represent the proxy as a
true underlying variability plus some measurement noise with known
characteristics. Hence filtering, smoothing and forecasting ideas can be
used to improve our estimates of variability by exploiting the time series
structure of the realised variances. This can be carried out based on a
model or without a model. A comparison is made between these two methods.
Keywords: Kalman filter; Mixed Gaussian limit; OU process; Quadratic
variation; Realised variance; Realised volatility; Square root process;
Stochastic volatility.