| VALUE-AT-RISK的核估计理论 |
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| 引用本文： | 朱宏泉,卢祖帝,汪寿阳.VALUE-AT-RISK的核估计理论[J].系统科学与数学,2002,22(3):365-374. |
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| 作者姓名： | 朱宏泉 卢祖帝 汪寿阳 |
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| 作者单位： | 中国科学院数学与系统科学研究院系统科学研究所,北京,100080 |
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| 基金项目： | 国家自然科学基金（NO.79930900）资助课题，中国科学院数学与系统科学研究院院长创新基金（1501800）资助课题. |
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| 摘 要： | 如何根据历史数据估计Value-at-Risk（VaR）;是风险分析与管理中一个重要的基本问题.木文基于非参数核估计方法,通过拟合实际数据过程的分布,构造了VaR的估计.在合适的相依数据条件下,证明了该估计量的渐近正态性,并给出了渐近方差的估计.由此表明:本文所构造的估计量不仅比参数模型具有更广泛的适应性,而且如同参数模型具有n~（-1/2）的收敛速度.本文假设的数据过程避免使用混合性,可很好地适用于金融管理中广泛应用的ARMA与GARCH模型族及非线性模型.
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| 关 键 词： | 风险 数据过程 核方法 VaR估计 渐近正态性 渐近方差 |
THE KERNEL ESTIMATION OF VALUE-AT-RISK: THEORY |
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| Hong Quan ZHU,Zu Di LU,Shou Yang WANG.THE KERNEL ESTIMATION OF VALUE-AT-RISK: THEORY[J].Journal of Systems Science and Mathematical Sciences,2002,22(3):365-374. |
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| Authors: | Hong Quan ZHU Zu Di LU Shou Yang WANG |
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| Institution: | Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080,P.R.China |
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| Abstract: | How to estimate Value-at-Risk (VaR) from historical data is a fundamental problem in risk analysis and management. In this paper an approach is proposed to estimate VaR by using kernel method to fit the distribution of the real data, and the computation is shown to implement simply. The asymptotic normality of the estimator is proved under suitably verifiable conditions which cover a lot of commonly used financial time series, e.g. ARMA and GARCH models. This property illustrates that the proposed estimator of VaR both enjoys the flexibility of non-parametrics and also shares the convergence rate of n~(1/2) with the parametric models. |
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| Keywords: | Risk data generating process kernel estimation VaR asymptotic normality asymptotic variance |
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