Research On The Stochastic Theory Of Option Pricing And Statistical Analysis Of Fluctuations In Securities

In this paper, the random jump is introduced into the price changing process; so that the new price changing process is closer to the actual situation. On the basis of the formula for pricing a European calls option within risk neutral condition and the problem of risk aversion are studied. Then research the data on Chinese stock market by means of mathematical statistics. There are two parts in this paper:Part I: Using branching process to describe the stock price process is a new way to study price option. But it does not take the random jump of price changing into account. In this part, the random jump of price changing is introduced into the price changing process. Under the improved model, the formula for pricing a European calls option within risk neutral condition is obtained. Finally, the collection of risk neutral risk neutral in a risk-averse market is obtained, further more, this collection is separately discussed in accordance with the value of the expects of the random jump.Part II: At present, the study of the related indicators of stock in the stock market has been very extensive and in-depth; however, most research is based on indicators of changes with time, while neglecting the mutual relations of stocks in the same time. The discussion in this part is based on the mutual relations of stocks on the same trading days. In this part, make the statistical analysis of the closing price and the turnover of shares in Chinese stock market from 2002-2006 with the application of the ZIPF-plot methods. The indicators which describe the characteristics of closing price and volume of stocks of each trading day are given. Further more discuss the statistical characteristics and the mutual relations of these indicators. Hope to make certain interpretation and analysis to the characteristics of the Chinese tock market.