VaR Calculation And Empirical Study

There are three commonly used methods for calculating VaR: Variance-Covariance Approach; Historical Simulation Approach and Monte Carlo Simulation. However, when it comes to practice, two problems we often meet are the volatility calculating and the dependent structure of a portfolio. So the improvement of VaR calculating method is an important topic in finance.Many models can be used to describe the characteristics of volatility. In this paper, we focus on Stochastic Volatility model. The sample we select includes exchange rate data of RMB from January 2008 to April 2010. After the analysis of statistic characteristics of USD/RMB and Euro/RMB, we use MCMC method under stochastic volatility model to calculate VaR and ES. The result shows the SV model can properly describe the characteristics of exchange rate volatility. Therefore, basing on this model, we can estimate the risk of exchange rate.In the past,we assume each asset is independent or conforming linear dependence when dealing with a portfolio. In this paper, we use Copula to deal with the correlation. The sample we select includes loss data of operation risk of Chinese banks from 1998 to 2008. Assuming every kind of loss satisfies the same distribution, we use Monte Carlo method to calculate the VaR and ES. The back-testing shows Copula can do with the corrections among assets well and the VaR based on Copula can reflect the operation risk well. So banks would then properly set the reserve.