VaR Calculation Based On Quasi - Monte Carlo Method And Its Empirical Study In Chinese Stock Market

With the continuous development of the global financial markets, the new financial products and financial business emerge constantly. At the same time, risk factors existing in the economic, social, and political areas are also increasing rapidly. Various types of financial institutions are facing more and more systematic and unsystematic risks. The recent global financial crisis also has exacerbated the people’s worries about the financial risk; weaken the faith of ordinary people for financial stability. As the managers and stakeholders of financial risks, in order to obtain the corresponding excess returns, financial institutions can’t completely avoid risk. They should try to reduce the loss at will through risk identification, measurement, inspection and control. In this background, the VaR, as a method of measuring portfolio’s maximum loss under a certain probability, has been used frequently.The traditional ways of calculating VaR include analysis method (also called variance-covariance method), historical simulation and Monte Carlo simulation. As a global valuing method, the application range of Monte Carlo simulation is very wide. It can be applied to nonlinear portfolio, non-normal random distribution and multi-dimensional risk factors. However, there are also some of the more obvious flaws about Monte Carlo simulation, such as low convergence rate and the phenomenon of ’pseudo random number’. These defects not only increases the amount of calculation of the Monte Carlo method, and at the same time reduces the accuracy of the VaR calculation. Therefore, this article tried to introduce the quasi-Monte Carlo method to improve on it. Quasi-Monte Carlo method is also known as low discrepancy sequence method.In the article, we built the basic steps of about the quasi-Monte Carlo method to calculate VaR. Then with the Shanghai composite index, using general error distribution for fitting, the empirical research was conducted on the convergence and accuracy. Through empirical research, we got the following conclusions:1, The distribution of stock market returns have fat-tailed features and general error distribution is a good way to fitting the probability density distribution function of stock market yields;2, in the process of calculating VaR, compared with the Monte Carlo method, quasi-Monte Carlo method has a faster convergence rate;3, after we have replaced Monte Carlo simulation method in the calculation with the quasi-Monte Carlo simulation method, the accuracy of the VaR calculation improve obviously. Quasi-Monte Carlo method under every confidence level can pass the failure frequency tests.