The Innovation And Pricing For Power Option

Since the appearence of B-S pricing formula at the beginning of 1970's,the option market has been developed quickly. On the base of standard option ,many exotic options are derived . Therefore, the essay of pricing on derivative securities now become an important problem, and be attentioned in financial mathematica.In this paper we assume that there exists a complete and continuous market model which consists of asset price be assumed to satisfy geometic Brown motion. A new option,named power option which change the payoff constructs,have more vivid than standord options,and adapt to different risk to lerauce for investors. And on the basic of power option,the pricing of the power barrier option and power lookback option are also discussed.By means of Martingle approach(risk-neutral valuation) to get the pricing of the option. Under Martingle measure,the pricing of a security(or derivative security) can be deduced by discount the expection of future cash flowing of the option,and the discount is under risk-neutral.We have main conclusions in this paper as follows:1. European quardratic option pricing formula is obtained,and on this basic we derive the pricing formula of power option.2.By apply of the pricing fomula of power call option, we get four pricing fomulas of power continuously barrier options(i.e.up-and-out,up-and-in,down-and-out,down-and-in) and two pricing fomulas in discrete case of up-and-out call and down-and-out put.3.By using the pricing fomula of the above,we also get two pricing fomulas of power lookback options(i.e.floating strick,fixed strick).4.Get two pricing fomulas of power lookback options(i.e.floating strick.fixed strick) with discrete and partial monitoring of the underlying price.