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.