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Pure Mathematics 2026
带跳随机波动率模型的非参数门限复加权估计
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Abstract:
本文采用复加权估计方法对带跳随机波动率模型进行非参数估计，并通过引入门限函数去除跳的影响。该方法既继承了局部线性估计量优良的偏差特性，又能在有限样本条件下保证对扩散系数的估计值非负。理论分析表明，温和条件下本文构造的估计量具有相合性和渐近正态性。
In this paper, the Reweighted Nadaraya-Watson estimation method is adopted for the nonparametric estimation of the stochastic volatility model with jumps, and the impact of jumps is eliminated by introducing a threshold function. This method not only inherits the excellent bias property of the local linear estimation, but also ensures the nonnegativity of the estimated value of the diffusion coefficient under finite sample conditions. Theoretical analysis shows that the estimator constructed in this paper is consistent and asymptotically normal under mild conditions.
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