Study On Pricing Look-back Option With Bonus Under The CEV Model

Financial derivatives occupy a very important position in today's financial markets,and the option is a very significant product of the financial derivatives.Research options has already begun in the very early.In the continuous development of economic society,the development of the options is also pretty fast,and today the option has been a very important and indispensable financial product.With the rapid development of financial markets and increasingly fierce competition,the financial structure continues to change dramatically and accelerates innovation.Therefore,the study of option is particularly important.And in the study of options what we must understand is exotic options,including a variety of exotic options.One of these options is that investors want to get the maximum value in the process of investing in options.The maximum is to get the maximum benefit.The exotic options what depends on the path is called look-back options.This paper at first introduces some basic concepts and history of the development of options,describes in detail the importance of options in the financial markets,as well as significance and status of option research.After the second chapter describes the basic knowledge to use when study options,such as the probability space,random process theory and Brownian motion,etc.Then there gives basic principles of option pricing model,and finally consider the reality of the financial condition by CEV model and we get the option pricing formula.In the current financial market Black-Scholes model is successfully solved the European option pricing under the efficient market.But it is established just under the certain assumptions,and in real trading,options investors will get some stock dividends at maturity.Based on the Black-Scholes model we research a class of dividend look-back Option Pricing of the CEV model.In this paper,the study of dividends from easy to difficult,first consider the case of dividends is constant,then further consideration dividend is a continuous function of time on the case,and then get the differential equation of continuous dividend of look-back option pricing under the model.