EM-based NIG Distribution And Its Application In Rates Of Return On Chinese Stocks

Traditionally, we used to use Gaussian distribution to describe the return rates of financial assets and many financial models were proposed based on the assumption. However, there are more and more scholars found that the financial data is not exactly following the Gaussian distribution. Shilong, Wu(1999), a scholar from China, did statistical quantitative analysis by using the sample of The Shenzhen Composite Index and found that the results showed price changes in Chinese stock markets actually does not follow Gaussian distribution. The sharp peak and heavy tail property in financial data has made it impossible to be described by the Gaussian distributions.Alien researchers found that Generalized Hyperbolic distribution better describes return rates of foreign financial assets. According to the fact of China, this thesis tries to show that volatility of Chinese financial data follows Normal inverse Gaussian distributions-a child class of Generalized Hyperbolic distribution. And then we use Monte Carlo simulation method to demonstrate reliability of the data fitting. Further, on the basis of foreign scholars, we use EM algorithm to estimate the NIG’s parameters and provide the detailed parameters estimating process and steps.