Forecasting The Stock Price With Hilbert-Huang Transforms And Pricing Option

This paper consists of three parts: forecasting the stock price by using Hilbert-Huang transforms, pricing of option, principle of the pricing of option applied to insecurance actuary.In Chapter 1,we introduce the development of theory of these parts.Up to now, we forecast mainly the stock price in the two ways, the pricing formulation and some methods of time series analysis. However, they have respectively disadvantages. For the first, the assumption being of efficient market is so strict that it is very difficult to apply the conclusion on the assumption to reality. As for the later, there are some methods for time series analysis, such as Fourier analysis, wavelet analysis, and so on. But, all of them also have disadvantages respectively. The Fourier analysis isn't valid in frequency and in time simultaneously. Though wavelet transform can valid in frequency and in time simultaneously , it is not of its adaptive nature. In Chapter 2 of this paper, we take use of a new method that is adaptive, high effective and practical for foreseeing the stock price. It is called as Hilbert transforms. Through analyzing Hilbert spectrum we forecast the stock price with ARIMA method.Since the financial derivative stock has the indispensable branch of financial market in the past time, it is very important to how to make the study of financial derive pricing theory more suitable to financial market on the theory basis built. In chapter 3, we study pricing of geometric average Asian capped calls, pricing of geometric average Asian option with transaction cost, pricing of the two kinds of exotic option in Fractional Brownian motion environment, pricing of capped calls with transaction cost in fractional Brownian motion environment.As a indipensable branch of financial field, insecurance is important for reducing risks in life. In chapter 4, firstly underling net premium principle, we apply the pricing of European call and capped call to the pricing of net premium with a deductible and underlying retention in the individual risk model. Then we take use of jump-diffusion precess for obtioning the price of net premium at any time before mature in the collection risk model.