Graduate Student Seminar: Statistical Inference for Integrated Volatility in the Presence of Jumps

Integrated volatility is a fundamental measure for assessing market risk and asset price dynamics, making its estimation a longstanding focus in stochastic process research. This presentation reviews existing statistical inference methods for estimating integrated volatility in the presence of jumps. While rate- and variance-efficient estimators have been developed for processes with jumps of bounded variation, the case of unbounded variation remains largely unaddressed. We propose a rate- and variance-efficient estimator for Lévy processes with a Blumenthal-Getoor index below 16/9. Our approach employs a multi-step debiasing procedure applied to the truncated realized quadratic variation.