A New Probability Model For Measuring The Risk

The Basel Agreement was regarded as the unified standard by All banking institutions on controling the risk. The key of it’s index was Capital adequacy ratio index. The accurate Capital adequacy ratio index depended on the risk measure of bank.Value-at-risk, one of the most commonly used methods of Financial portfolio risk measurement, was originally proposed and broadly used by J.P.Morgan and G30 in 1993. Now, it becomes the foundation of financial risk management which is mainly adopted by banks.Conventionally, people calculate VaR under the assumption that the log return series of the portfolio of the relevant assets follow the Gaussian law. However, many empirical studies suggest that the following stylized characteristics broadly exist in the financial time series: their probability density distribution are skewed to the left and fat tailed, the volatilities of the series are clustered and have leverage effect and the return series with different frequency demonstrate Aggregational Gaussianity.This means if we calculate the VaR under normal assumption, then we will underestimate the risk. On the other hand, if we calculate VaR based on t-distribution,which is a common candidate to substitute normal distribution by some people, we will over estimate the risk. Therefore, finding a distribution that can well fit the log return distributions is crucial for building a risk model. Jiang(2000) has proposed two class of distributions to model the log return series in financial market. The new distributions have performed very well in both domestic and international financial market. In this paper, we will use the GARCH technique together with these two distributions to create new models for calculating the VaR and deal with the parameter estimation problem in the model. In addition, we will carry out some investigations of how well our new model work comparing to the model with normal or t-distribution as key building blocks.When caculating the stat VaR, we discover that compared with under the Normal and t distributuion, the value of VaR under the assumption of new distribution, is more closed to that of Empirical distribution. Caculating the dynamic VaR, the value of VaR, under the Shanghai Composite Index’s return series is Quantile-GARCH Class I distribution, can pass the Kupiec test when the value of Confidence level is97.5%. When the object is SZSE Component Index’s return series, the dynamic VaR can pass the Kupiec test at the value of 99%. The result shows that the dynamic VaR of the Quantile-GARCH Class II distribution can pass the Kupiec test at any value of Confidence level. It can describe the financial return series better.