Master's in Statistics Oral Defense: "Spot Volatility Estimation of Itō Semimartingales Using Delta Sequences"

Abstract: This thesis studies a unifying 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 asymptotic theory is derived with unevenly sampled observations under infill asymptotics and fixed time horizon are considered, and the state variable is assumed to follow a Brownian semimartingale. Then the thesis extend the class of estimators to include Poisson jumps or financial microstructure noise in the observed price process. High-frequency data is simulated to make a comparison when using different delta sequences . As application, specific delta sequences are applied to data from the APPLE stock index market.

Advisor: Todd Kuffner

Thesis Advisor: Jose Figueroa-Lopez