This thesis studies the nonparametric estimation of spot volatility and integrated volatility functionals from high-frequency observations of a continuous Itô semimartingale. The work is motivated by the structural analogy between classical kernel smoothing in nonparametric statistics and time-domain smoothing of squared high-frequency increments in financial econometrics. In particular, while kernel-based spot volatility estimators of Nadaraya--Watson type are natural and widely used, they are known to suffer from non-negligible boundary effects. To address this issue, this thesis introduces a normalized local linear estimator for the spot volatility process. The proposed estimator incorporates the local linear moment correction through weights together with an explicit normalization term designed to stabilize the induced weight structure and preserve good behavior over the full observation interval, including the neighborhoods of the time boundaries. Based on this construction, the thesis studies the plug-in estimator for the integrated volatility functional. 

The thesis makes both numerical and theoretical contributions. On the numerical side, a simulation study under a stochastic volatility model compares the proposed local linear estimator with a naive local constant Nadaraya--Watson benchmark. The Monte Carlo evidence shows that the two estimators behave similarly in the interior of the sampling window, whereas the proposed local linear estimator exhibits substantially smaller mean squared error near the left and right boundaries. This finite-sample behavior is consistent with the classical nonparametric intuition that local linear smoothing reduces boundary bias. 

On the theoretical side, the thesis develops a detailed decomposition of the standardized estimation error into five terms, which respectively capture the discretization error, the leading stochastic fluctuation, the first-order bias inherited from spot-volatility estimation, the second-order Taylor contribution, and the effect of the normalization term. This decomposition allows the asymptotic behavior of the estimator to be analyzed term by term. In particular, the leading term is shown to retain the mixed normal limit familiar from the existing kernel-based plug-in literature, while the remaining terms generate explicit asymptotic bias corrections involving the kernel, the local linear boundary functions, and the covariance structure of the volatility process itself. The normalization component contributes additional endpoint terms that make the boundary effect fully explicit. Taken together, these results yield a biased central limit theorem for the proposed plug-in estimator and clarify how the local linear correction modifies the asymptotic bias structure relative to normalized Nadaraya--Watson-type estimators. 

Overall, this thesis extends the classical local linear smoothing methodology to the high-frequency spot-volatility setting and shows that it provides a theoretically tractable and numerically advantageous alternative for the estimation of both spot volatility and general integrated volatility functionals. The proposed framework contributes to the intersection of nonparametric smoothing theory and modern high-frequency financial econometrics by combining boundary-bias reduction, explicit normalization, and a full term-by-term asymptotic analysis within a local linear approach.