This paper is based on the suppose of Black-Scholes. By using the risk neutral pricing theory of option and analysising the martingale property of the asset value process, we construct the model of the value of barrier options. By solving the heat equation, we obtion the price of the barrier options. Meanwhile, to the curve boundary and double constant boundarys, we obtain the probability distribution function of the time which the value of underlying first reach the boundary before maturity date by using equivalent martingale measure, reflection theory and residue theorem. On the other hand, we discuss the situation of paying a sum of cash when the option is knocked out and knock-in options. We also discuss how to make use of the option pricing in the pricing of other derivatives. |