Estimation And Calculation Of VaR And CVaR

In the background of the financial globalization, financial risks management is a hot topic for recent years. So, financial risks management is a hot topic in financial institutions, academia, and financial supervisors. Risks measurement is the core of effective risks management. Therefore, it is significantly important to study risks measurement in the background of financial globalization. Reasonable risks measurement is fundamental for China's risk management study. In this paper, we discuss Value at Risk (VaR) and Conditional Value-at-Risk (CVaR) mainly. These risk measurements set their bases on statistics and mathematical algorithms, combined with marketable movement. In this paper, we will use quantitative analysis more than qualitative analysis. The main works of this paper are as follows: 1. There are some introductions on the two modern risk measurements. Each risk measurements'definitions, properties, calculation and appraisement arithmetic are introduced; 2. In this paper, statistical method is put forward to improve the estimation of VaR and CVaR. These methods avoid burdensome simulation calculating and parameters estimate. This paper discusses the excellent estimation of VaR and CVaR for asset under normal distribution and gives the uniformly minimum variance unbiased estimate (UMVUE),the best linear unbiased estimate (BLUE) and the best linear invariant estimate (BLIE) of VaR and CVaR. Furthermore, we show the practicability and validity of these methods. 3. This paper determines the Confidence Interval and completes the hypothesis test of CVaR for asset under normal distribution. Then, the methods and relevant results are used to make empirical analysis of CVaR of Chinese stock market. 4. The actual distribution of asset returns possesses the characteristic of steep peaks and heavy tails, so traditional normal distribution cannot describe this characteristic any longer. In this paper, laplace distribution is put forward to fit the date of asset returns, and then we study and provide an analytical formula and estimator for VaR and CVaR, calculated for laplace distribution. The methods and relevant results are used to make empirical analysis and calculation of risk of stock market in the end. At last, we mentioned the directions of the further research.