A Study On Two Exotic Options Pricing Under Jump-diffusion Model

Financial mathematics is a new developing branch of science, it is now being paid close attention to in the domain of international finance and applied mathematics. Uncertain pricing is one core of financial mathematics study, it involves the theories of modern finance such as asset pricing theory, investment combination theory and it involves theories of modem mathematics such as stochastic analyzing and optimizing theory too. Effective management of risk occupies the right evaluation of derivative securities. The critical thing is that the financial derivative securities exist reasonably and develop properly is how to value its fair price. Recently, in addition to known European options andAmerican options , there appear many new variety which are changed, composed, derived by vanilla options in international financial market. This dissertation is intended to study option pricing problems, so as to establish the mathematic model of option pricing with jump-diffusion process by means of mathematical tools such as martingale theory and stochastic analysis, to deduce continuous strike call options,Barriers options pricing when stock price driven by jump-diffuse process.The chapter 4 is based on the theory of the risk-neutral. Under the stocks process is driven by Poisson jump-diffusion, and the jump-height is constant, using Girsanov theorem, the only equivalent martingale measure is obtained, and the pricing of continuous strike options on jump-diffusion model are obtained by martingale method in a complete market.The chapter 5 is based on the theory of the risk-neutral. Under the stocks process is driven by Poisson jump-diffusion, and the rate of expected stock-returns, fluctuating rate and risk--less rate are function of time are constant, using Girsanov theorem, The Pricing of European options on jump-diffusion model were given.