Value‐at‐Risk under Measurement Error
提出一种校正股票价格测量误差的风险价值估计方法，解决现有估计不一致导致风险低估和极端杠杆的问题，通过傅里叶变换和反卷积核密度估计实现稳健估计。
We propose a method for estimating Value‐at‐Risk that corrects for the effect of measurement errors in stock prices. We show that the presence of measurement errors might pose serious problems for estimating risk measures. In particular, when stock prices are contaminated, existing estimators of Value‐at‐Risk are inconsistent and might lead to an underestimation of risk, which can result in extreme leverage ratios within the held portfolios. Using a Fourier transform and a deconvolution kernel estimator of the probability distribution function of actual latent prices, we derive a robust estimator of Value‐at‐Risk in the presence of measurement errors. Monte Carlo simulations and real data analysis illustrate satisfactory performance of the proposed method.