The Research Of Quantitative Analysis On Stock Bubbles

The research on stock market bubbles is an updating topic of current economical and financial fields, which has significant meaning for risk investment and healthy, stable development of stock market. Currently, in academic circle, both overseas and domestic scholars have made some staged achievement in this research topic.Scholars have made some research on stock bubbles. Firstly, qualitative analysis researches have applied in this field to test the existence of stock bubbles, and achieve some methods for testing. There are two types of testing, direct test and indirect test, including run test, variance bounds test, unit root test, etc. Secondly, some quantitative analysis methods are applied to research bubbles, including P/E ratio measure, P/B value ratio measure, bubble coefficient measure, etc.The word, stock bubbles, is used very early, but even now no one has given it an exact, uniform definition, and has the measuring mathematical model, which is acknowledged. However, there is a common belief in academic circle, i.e. bubble refers to a situation in which the market value of a financial asset exceeds the present value of the dividend stream associated with that asset. Even so, different scholars have different definitions for stock bubbles. A new try to the definition of stock bubbles has been used in this paper. Dividend discount method is utilized to explain the stock intrinsic value (or fundamental price) and the definition of stock bubbles is given based on stock intrinsic value. First of all, we build the binomial trees model of dividend, through discounting the future dividends to calculate the intrinsic value of stock, and then we get the stock bubbles model according to the definition of bubble. Through introducing a critical value of stock price whether there is dividend or nor, the bubble model is improved to be more matching to reality. Secondly, we build the GBM model of dividend, which is another method to study bubbles. From the GBM model of dividend, we could calculate the intrinsic value of stock, thus we have another stock bubble model. Meanwhile, related similar improvement is made in this model.