Study On Value At Risk Based On Bayes Estimation And Extreme Value Theory

In recent years, financial extreme event happens frequently. The financial market lies tremendous extreme risk, which is a kind of market risk and will cause great losses once it happens, although it seldom happens. Therefore it is very important that the financial extreme risk is measured accurately. VaR technology was born in 20th century 90's. Now it has had application in risk measurement of kinds of financial instruments, and become mainstream measurement standard in the international financial market. The common VaR measurement methods mainly include historical simulation method , variance-covariance method and Monte Carlo method. These methods all have only application in measuring losses under the normal market condition, but not the losses under extreme capital gains.The extreme value theory specialises in the extreme value distribution characteristic of ordinal statistic. POT model is one of the common models in EVT. It makes model for the data exceeding a sufficiently large peak, and it does not require to suppose a given distribution for the whole data. Because the distribution tail is depicted by data itselves, the model risk is reduced. Calculating VaR through POT model can better depict the tail of practical financial data to calculate VaR exactly. In the process of calculating VaR through POT model, parametric estimation in model is vital. The paper does a trial research at this field.At first, using Bayes estimation method estimate the two parameters in the model. In the financial market, because the factors influencing return on assets is changeable, the parameters also changes constantly. Therefore, it is reasonable to count the parameters as random variable. The Bayes estimation method combines prior information with sample information through counting the parameters as random variable, so it conquers the difficulty of short of sample data. When measuring the extreme VaR through integrating Bayes idea into extreme value model, investors will simultaneously take into account posterior information and observed sample information to make the value of VaR more modest.Secondly, in the process of calculating Bayes estimation of parameters, MCMC method is used. MCMC method acted as a simple and effectual Bayes calculating method can transform some intricate high-dimensional problems to a series of simple low-dimensional problems. The paper will use one of the most simple, the most widely used MCMC methods——single-site Gibbs sampler.Finally, the ideal result is gained through analysing Shenzhen Composite Index practically. That proves the model to be effectual to some extent.