Candidacy oral presentation: Statistical Inference for Integrated Volatility

Abstract: Integrated volatility serves as a crucial measure for understanding market risk and asset price dynamics, making its estimation a longstanding focus in stochastic process research. This presentation provides an overview of existing statistical inference methods aimed at estimating integrated volatility in the presence of jumps. While several rate- and variance-efficient estimators have been proposed for processes with jump of bounded variation, the challenge of jumps with unbounded variation remains largely unexplored. In our preliminary results, we construct a rate- and variance-efficient estimator for the Lévy process with Blumenthal-Getoor index less than 16/9. The proposed method is based on a multi-step debiasing procedure for the smooth truncated realized quadratic variation of the process.

Committee members: Nan Lin and José E. Figueroa-López