Generalization And Application Of European Barrier Options In Jump-Diffusion Model

Options are the core tool of risk management.Early in1973, Fiseher Black and Myron Scholes Proposed a famous option Pricing model—B-S model.Afterwards following years,option Pricing theory has developed quickly.Recently, in addition to known European options and American options, there appear many new variety which are changed,composed, derived by vanilla options in international financial market.Barrier options are one of these new options.Benefits of Barrier options attached to the price of the underlying asset at a specific period of time whether it reach an agreed level. During the validity period of the options, if the price of the underlying assets achieving the agreed price (barrier level), the option will take effect or failure. The assumption of most model in the pricing of barrier options is that whether the underlying asset reach the fixed level in the continuous observation, in reality, however, random barrier level can meet the requirements of investors’risk hedging. And the research of variable barrier level in jump diffusion model is also valuable in the process of real options pricing, and variable barrier level can reflect the true value of an investment project.In this paper, the results are as follows:First, The assumption of most model in the pricing of barrier options is that whether the underlying asset reach the fixed level in the continuous observation, in reality, however, random barrier level can meet the requirements of investors’risk hedging.so in this article we relax the assumption of barrier level is a fixed value, discuss barrier option pricing when barrier level is H(1+h)N(?)ert and derive the pricing formula of European barrier options in jump-diffusion model.Second, The application of real options becomes more and more widely in the actual life, the defects of traditional method to evaluate investment decisions is obvious, such as net present value (NPV) method, the octree method, etc.we research barrier option pricing problems when barrier level is variable in this article, the results also can be used in the actual investment decisions. So we discuss the application in the real estate investment decision-making under the condition of random barrier level in the last part of this article.