基于扩散过程核权r阶幂变差瞬时波动率估计的VaR度量

Measurement of Value at Risk Based on Kernel-Weighted r-Power Variation Estimation of Instantaneous Volatility for Stochastic Diffusion Model

摘要: 在金融市场中，收益率序列的波动性往往与金融资产的风险挂钩。因此，VaR作为被普遍认可且有广泛应用的资产风险度量指标，在利用参数法对其进行计算时，波动率是其中重要的输入变量。本文在对数收益率服从随机扩散过程这一假设下，利用r (r > 0)阶幂变差构建瞬时波动率核估计，证明其渐近无偏性，并进一步通过数值模拟来考察由该瞬时波动率估计所计算的VaR在有限样本下的表现。结果显示：在显著性水平为5%的情形下，利用Kupiec检验法对随机扩散过程假设下的VaR结果进行回测检验，所得统计值落在非拒绝域内。由此可见，利用该方法在随机扩散模型下计算出的VaR是可靠的，可用来有效估计资产投资组合的风险。

Abstract: The risk of financial assets is related to the volatility of return in the financial market. Therefore, when we estimate VaR, which serves as a widely used measurement of assets’ risk, with parametric method, volatility is one of the most important input variables. In this paper, we proposed kernel-weighted estimators of instantaneous volatility with r (r > 0)-power variation for stochastic diffusion model, proving its asymptotic unbiasedness. A simulation study will examine the finite sample properties of the VaR estimated by the estimators we proposed. It is shown that the VaR we estimated passed the test of significance, which means it is reliable to be the measurement of assets’ risk.