Study On Power Option Pricing Under The O-U Process

Option pricing is one of the important elements of financial mathematics and economics,the research and development of option pricing have far-reaching impact on finance and capital markets.In recent years,with the exception of European and American options,a large number of new financial derivatives are derived in the international financial derivative market.Among them,the power option is one of the new typical options.The research of the power options has the significance meaning on both theoretical and practical.For different risk tolerance of investors,the unique advantages of power options can satisfy the need of investors,and inject new vitality to the research of financial markets,it also provide more investment options for the majority of investors,so this paper mainly studied the power options pricing model.This paper introduces the development of option pricing and its related concepts,the basic knowledge of stochastic processes that are related to this article have been described in detail.Introduce three kinds of commonly used method of numerical calculation,and the simulation of the process of the stock price.The main content is according to the stock price follows O-U process which can reflect the excepted rate of return of stock volatility.In the first consider the case of non-payment of dividend,using the actuarial method,we obtain the pricing formulas of power option with stochastic interest rate or change exercise price.Then consideration dividend is a continuous function of time t,and get the pricing model.Compared to other methods,stochastic integral method is easier to understand.It provides a new method of pricing for the financial market.