Spot Volatility Estimation Using Delta Sequences

We introduce a class of nonparametric spot volatility estimators based on delta sequences and conceived to include many of the existing estimators in the field as special cases. The full limit theory is first derived when unevenly sampled observations under infill asymptotics and fixed time-horizon are considered, and the state variable is assumed to follow a Brownian semimartingale. We then extend our class of estimators to include Poisson jumps or financial microstructure noise in the observed price process. As an application of our results, we relate the Fourier estimator to a specific delta sequence obtained with the Feje'r function. The proposed estimators are applied to data from the S&P500 stock index futures market.