Abstract:

The pricing of a new kind of option,barrier option,is discussed in this paper.The general discussion about barrier options usually concerns a relatively simple situation,that is,the option barrier is constant.However,the barrier actually changes with time.Because of this,the backward stochastic diferential equation and the equi-valent martingale are used to get a group offormulae for pricing the Europe an down·-and·-out call options with the hy-pothesis that the barrier is dependent on time.

Key words: barrier option, option pricing, equivalent martingale measure, backward stochastic diferential equa-tion