NONPARAMETRIC ESTIMATION OF VOLATILITY FUNCTIONS: THE LOCAL EXPONENTIAL ESTIMATOR
提出局部指数估计量来估计条件波动率函数，保证非负性，证明其渐近性质优于局部线性估计量，且对未知条件均值函数完全自适应，模拟研究显示其表现更优。
Kernel smoothing techniques free the traditional parametric estimators of volatility from the constraints related to their specific models. In this paper the nonparametric local exponential estimator is applied to estimate conditional volatility functions, ensuring its nonnegativity. Its asymptotic properties are established and compared with those for the local linear estimator. It theoretically enables us to determine when the exponential is expected to be superior to the linear estimator. A very strong and novel result is achieved: the exponential estimator is asymptotically fully adaptive to unknown conditional mean functions. Also, our simulation study shows superior performance of the exponential estimator.