在金融市场风险管理研究中,利用参数及半参数模型度量风险价值并不足以体现投资行为的异质性及资产价格波动的多尺度特征. 引入概率密度的小波非线性阈值估计方法,建立了风险价值的多尺度估值模型,并分析了估值误差的收敛性, 发现密度函数空间的光滑度和样本容量同时决定均方误差的收敛速度. 最后以正态密度函数为算例,通过不同容量的仿真样本检验了该理论方法的可行性.

It was insufficient to reflect the heterogeneity of the investment behavior and multi-scale features of the asset price fluctuation via using the parametric or semi-parametric models to measure the market risk in financial risk management research. This paper introduced the probability density of nonlinear wavelet threshold estimator in order to establish the multi-scale valuation model of the Value-at-Risk and analyze the mean square error (MSE) convergence of the model. The result shows that both the smoothness of the density function space and sample size determines the MSE convergence rate. Finally, by means of different sample sizes of simulation experiment, we choose the normal density family as an example to prove the feasibility of the proposed approach.