一类重尾风险因子的模拟及其投资高风险值和置信区间的估计

由于金融市场中的日周期或短周期对数回报率的样本数据多数呈现胖尾分布，于是现有的正态或对数正态分布模型都在不同程度上失效，为了准确模拟这种胖尾分布和提高投资风险估计及金融管理，本文引进了一种可根据实际金融市场数据作出调正的蒙特卡洛模拟方法．这个方法可以有效地复制金融产品价格的日周期对数回报率数据的胖尾分布．结合非参数估计方法，利用该模拟方法还得到投资高风险值以及高风险置信区间的准确估计。

Simulation and Extreme VaR and VaR Confidence Interval Estimation for a Class of Heavy-Tailed Risk Factors

This paper introduces a calibrated scenario generation method to estimate extreme Value-at-Risk (VaR) and Value-at-Risk confidence interval (VaR CI) of a portfolio with single risk factor which has heavy tailed distribution. It is well known that lot of financial, daily log-return data demonstrate heavy-tailed distribution. This makes all the models with normally, even log-normally distributed assumption become disabled (see 25]). We handle the daily return data with heavy tailed distribution and use a model of log-mixture of normal distributions to calibrate mean, variance, kurtosis, and sixth moment and fit the empirical distribution. An extreme value is a rare event and not easy to be observed. However, once it occurs, it brings disaster to any involved financial institute and financial practitioners. Therefore, undoubtedly how to effectively estimate the portfolio extreme VaR and VaR CI is a primary concern in risk management. In this paper, we will use a non-parametric method to derive portfolio extreme VaR and VaR confidence interval estimates for heavy-tailed distributions based on scenarios which are generated with calibration.