The Research Of Option Pricing About Different Financial Market Models

The thesis focuses on the option pricing method about different financial market models,mainly for the method of pricing jump-diffusion power options and binary options in incomplete markets.There are standard Brownian motion,mixed fractional motion,random paying dividends and stochastic interest rate associated with the financial market models.The financial derivatives market is developing rapidly in recent years.Many scholars make further progress on financial markets.Then it leads to the elimination of mass different financial market models.We use diverse ways to handle the options in incomplete markets according to different financial markets and obtain the results of options pricing.By means of different modelings,we can find the advantages and disadvantages of different methods and probe the financial model meanings.Since the capital market mechanism established in our country,the option research has been a hot topic with many published articles and books.In the thesis option pricing will be studied based on claimed achievements.There are six chapters in the thesis.The first and second chapters are the introduction and preliminary knowledge.They contain some important formulas and theories.In the third chapter,we assume that the prices of stocks follow jump-diffusion motions and the stocks have dividend-paying and stochastic interest rate.By introducing zero coupon bonds,we use general martingale measure to attain the price of the power options in the incomplete market.In the fourth chapter,we make a model with floating exchange rate.Then we use insurance actuary pricing to calculate the jump-diffusion power options pricing.In the fifth chapter,we study the model of jump-diffusion power options under the condition of mixed fractional motion.We try to build a realistic market model in order to get the practical pricing result.Finally,we explore a multidimensional model in an incomplete market according to the example of binary options.The aim is to get the pricing result by the method of matrix transformation.