Estimation of the variation of prices using high-frequency financial data
When high-frequency data is available, realised variance and realised absolute variation can be calculated from intra-day prices. In the context of a stochastic volatility model, realised variance and realised absolute variation can estimate the integrated variance and the integrated spot volatility respectively. A central limit theory enables us to do filtering and smoothing using model-based and model-free approaches in order to improve the precision of these estimators. When the log-price process involves a finite activity jump process, realised variance estimates the quadratic variation of both continuous and jump components. Other consistent estimators of integrated variance can be constructed on the basis of realised multipower variation, i.e., realised bipower, tripower and quadpower variation. These objects are robust to jumps in the log-price process. Therefore, given adequate asymptotic assumptions, the difference between realised multipower variation and realised variance can provide a tool to test for jumps in the process. Realised variance becomes biased in the presence of market microstructure effect, meanwhile realised bipower, tripower and quadpower variation are more robust in such a situation. Nevertheless there is always a trade-off between bias and variance; bias is due to market microstructure noise when sampling at high frequencies and variance is due to the asymptotic assumptions when sampling at low frequencies. By subsampling and averaging realised multipower variation this effect can be reduced, thereby allowing for calculations with higher frequencies.