跳-扩散模型中即时波动率的门限多次幂变差核估计

Threshold Multipower Kernel Estimation of Spot Volatility for Jump-Diffusion Models

讨论了跳-扩散模型中即时波动率的非参数估计问题.基于门限技术与多次幂变差,构造一个门限多次幂变差核估计量,并在一些假设条件下,建立了估计量的相合性和渐近正态性.数值模拟分析了门限多次幂变差核估计量的有限样本表现.

In this paper,we propose a nonparametric estimator of spot volatility when the process is described by a jump-diffusion model.The newly defined estimator is based on the joint use of realized bi-power variation and the threshold technique,and is not only consistent,but also scarcely plagued by small sample bias.The consistency and asymptotic normality of the proposed estimator are established under mild conditions.Finally,a simulation study is undertaken to assess the finite sample performance of the proposed method.