This dissertation studies volatility estimation using high-frequency financial data. The primary focus is on estimation of spot volatility and integrated volatility in continuous-time models with jumps. While classical high-frequency methods perform well in relatively simple settings, highly active jumps create substantial statistical challenges because they distort the local behavior of observed price increments and interfere with recovery of the underlying continuous volatility component. To address this difficulty, the dissertation develops new methods based on kernel localization, smooth truncation, and recursive debiasing techniques. The proposed approaches improve the accuracy and efficiency of volatility estimation in the presence of highly active jumps while remaining explicit and practically implementable. Together, the results contribute new methodology and theoretical understanding for high-frequency volatility inference under realistic jump behavior commonly observed in financial markets.

Thesis Advisor: José E. Figueroa-López