The Research On VaR With Stable Distribution

Right investment decision requires reliable predictions of return and risk. Reliable predictions can only be obtained if the underlying statistical model tests on realistic assumptions.The distribution form of returns on financial assets has important implications on theoretical and empirical analysis in economics and finance.For example, assert portfolio and option pricing theories are typically based on distribution assumption that assert returns follows a normal distribution. However,researchers have found through their studies that the empirical distributions of asset returns are probably skewed and moreover that they often have "fat-tails ",because of the extreme market moves which seem to occur more frequently than the normal distribution could predict.The first attack on the assumption that asset returns are normally distributed was made by Mandel-brot.Mandelbrot had not only rejected the normal assumption,but also proposed an alternative distribution for modeling asset returns.This is alpha-stable distributions that allows skewness and heavy tails.The stable distribution is able to capture the two main characteristic of empirical evidence.In the dissertation,we analyze the use of stable distributions in VaR modeling and discuss the stable distribution of the stock index returns of Hongkong stock index futures market. The main contents and results are as following:1.The basic theories of univariate stable distribution and multivariate stable distributions and stable stochastic processes are introduced.2.The basic principle and main methods of VaR computation are introduced.3.Makes demonstrational analysis of the application of stable distribution to Hong Kong stock index future market.4.Stable Modeling of VaR is researched and VaR under the stable distribution is researched in HongKong stock index future market:one of the important questions is the validity of the model.Because VaR under the stable distribution are statistical and prediction model base on the history data or the presumed statis- tical parameter and distribution ,whether it can predict the risk correctly or not must be tested.The main method is back testing. Applying this statistical model to VaR test ,the real profit and loss data of financial asset is constructed to the prediction in a period to test the validity of VaR.Through the Backing test of HongKong stock index future market under the two model of normal distribution and stable distribution,the result shows that the VaR model can measure the risk of stock index future market in HongKong more accurately.