Spot Volatility Estimation of Ito Semimartingales Using Delta Sequences

OF THE Spot Volatility Estimation of Itô Semimartingales Using Delta Sequences by Weixuan Gao Master of Arts in Statistics Washington University in St. Louis, 2016 Professor José E. Figueroa-López, Chair Abstract: This thesis studies a unifying class of nonparametric spot volatility estimators proposed by Mancini et. al.(2013). This method is based on delta sequences and is conceived to include many of the existing estimators in the field as special cases. The thesis first surveys the asymptotic theory of the proposed estimators under an infill asymptotic scheme and fixed time horizon, when the state variable follows a Brownian semimartingale. Then, some extensions to include jumps and financial microstructure noise in the observed price process are also presented. The main goal of the thesis is to assess the suitability of the proposed methods with both high-frequency simulated data and real transaction data from the stock market. In conclusion, double exponential kernel shows the best properties when estimating. Besides, the theorem is robust with the presence of jumps and microstructure noise and the U-shape curves of intraday spot volatility are achieved. Keyword: Spot volatility, High-frequency estimation, Delta sequences, Microstructure noise, Kernel estimator vii Chapter