Font Size: a A A

The Statistical Analysis Of Stochastic Processes In Stock Market

Posted on:2008-04-06Degree:DoctorType:Dissertation
Country:ChinaCandidate:W LiuFull Text:PDF
GTID:1119360212491404Subject:Probability theory and mathematical statistics
Abstract/Summary:PDF Full Text Request
Many methods to analyze stock price have been developed since the capital market appeared. Through the application and development for more than 100 years, the technical analysis and basic situation analysis have become two important investment directions in the financial market. The technical analysis is based on the historical data of the information in stock market, which can predict the fluctuation of stock price in the future and guide people how to bargain. The tool in technical analysis is technical indicators. As a kind of investment means, the technical analysis gets an extensive applications in actual instruction. However, because of being lack of perfect theoretic foundation for a long time, the technical analysis is always regarded as a kind of subjective judgment. So the discussion about it is always hot, the issue of which is the effectiveness of the technical analysis is true or not.This paper proves that the technical analysis of the stock market can be explained by the stationary process theory, namely, the validity of some indicators can get interpretation from the existing stock price model (for example Black-Scholes model and stochastic volatility model). In the stock market, actual technical analysts look the stock prices everyday as one sample and according to the frequency of occurrence of a certain phenomenon they predict the developing trend of stock price. A lot of technical indicators are created by this way. For example, BOLL, RSI, ROC. However there is a problem which can not be ignored, namely all these stock prices are not independent. So up to now there isn't any statistical theory can be used to support technical analysis. In financial mathematics, a series of stock prices is regarded as a sample path of stochastic process. Thus the realization of these stock prices is only an event with zero probability. But we discover that, those most important technical indicators are all stationary processes or their functional transformations. However, stationary process can be computed the frequency is well known. From this point, we provide the theoretic basis for technical analysis of stock price. The paper is totally divided into seven parts to go on.In the first part, we review the existing analytical methods in stock market, introduce the definition and developing course of technical analysis and basic situation analysis. We set forth the methods which have been used by the actual technical analysts in stock market and academicians who engaged in related financial theory research. Finally, we put forward the main research way in this paper.In the second part, we introduce two kinds of continuous models, i.e. Black-Scholes Model and stochastic volatility model, which can be used to describe stock price behavior and are popular in financial mathematics. We introduce the development background of these models and give the concrete formula expression in this paper.In the third part, several technical analysis indicators (BOLL, RSI, ROC) are introduced, including the definitions and the applied rules in guiding bargain. We adopt three important stocks in American stock market (DIA, QQQQ, SPY), and give the statistical result in their technical analysis data.In the fourth part, based on the Black-Scholes model, we show some properties of the stochastic processes drawn from the technical analysis indicators. The related laws of large numbers are also discussed.In the fifth part, based on the stochastic volatility model, we provide the definition and related law of large numbers of one kind of asymptotic stationary process when some conditions satisfied. Some properties of the stochastic processes drawn from the technical analysis indicators are also discussed.In the sixth part, we give the distributional histogram plots of a series of stationary processes based on the Black-Scholes model. The corresponding distributional histogram plots of actual data are also shown.And in the last part, we do some tests on stock price model. We reject the hypothesis that stock price follows exponential Levy process. Moreover, we list some problem unsolved in our research.
Keywords/Search Tags:Black-Scholes Model, Stochastic Volatility Model, Stationary Process, Asymptotic Stationary Process, Technical Analysis, Bollinger Bands, RSI, ROC, Hypothesis test
PDF Full Text Request
Related items