The Calculation And Empirical Analysis Of VaR And CVaR Based On Important Samping

VaR (Value-at-Risk) and CVaR (Conditional Value-at Risk) are two important risk measures in the areas of identify, estimate and analyze risk in today’s society. They are have been widely used in the world. However, VaR has some shortcomings. It provides no information about the loss that investors might suffer beyond the VaR. Moreover, it has also been criticized for not being a coherent risk measure because it is not subadditive and often ignoring the actual value exceeds the threshold analysis. In the view of statistical, VaR is only a quantile corresponds to a certain confidence level, and it didn’t explore the information below the quantile, can’t accurately portray the risks. The CVaR satisfies the subadditivity and is coherent risk measure, CVaR can more fully describe the characteristics of the loss than VaR. CVaR model can overcome the defect that the VaR model exists. Therefore, in this paper we consider both of them at the same time to complement each other.In order to improve the precious of the VaR and CVaR model to measure the risk, many researchers at home and abroad have make a large amount of research on these factors such as:the distribution of the financial market variables, volatility estimation method, calculation method of the model. In terms of the distribution of the financial market variables, researchers put forward using geometric Brownian motion, the ARMA model, the generalized error distribution, skewed T distribution to fitting the changes of variable in the process; In terms of volatility estimates, some researchers have developed the ARCH model, GARCH model and ARMA-GARCH model to capture the volatility information, solving the problem of volatility clustering; The researchers’ research methods mainly include:the variance-covariance method, the historical simulation method, the Monte Carlo simulation method and so on. However, the occurrence of financial market risks, especially financial crisis is a rare event. To calculate the rare event requires a large number of samples, this increases the complexity of the problem, but the above three methods have failed to solve the problems existing in estimating the rare event. Variance reduction techniques are often used to increase the efficiency of the estimation. In this article we attempt to apply a kind of variance reduction technique-important sampling in the Monte Carlo method. Important sampling can allocate more samples to the tail of the distribution that is most relevant to the estimation of VaR and CVaR.In this paper, we choose the ARMA model fitting the rate of yields of the stock portfolios, and we using computer to generate the random number of the target time, and then we using the traditional Monte Carlo simulation and the Monte Carlo method based on important sampling to compute the VaR and CVaR of the stock portfolio respectively. At last, we make a comparison between the calculation results. And found that with the increase of the confidence level, the results of the improved Monte Carlo simulation method are more close to the true value than the results of traditional Monte Carol simulation method. This shows that the important sampling method to estimate the probability of rare events is more effective.