Barrier Options Pricing Theories

Barrier options are actually conditional options , dependent on whether some barriers are breached within the lives of the options. They are therefore path-dependent. Barrier options are geared to the needs of sophisticated investors , because these options are created to provide risk managers with cheaper means to hedge their exposures without paying for the price ranges that they believe unlikely to occur. The text target is to look for the price formulas of the barrier options. The thesis chapter 1,introduced the finance development situation, barrier options and reflection principle theorieses. The thesis Chapter 2,introduced Black-Scholes option price formula. Chapter 3, the emphasis of this paper, mainly discusses the pricing formulas of three kinds of barrier options. Firstly we discuss the pricing formulas of the options with barriers during the whole effective period of the options .Then we discuss the pricing formulas of the early-ending barrier options with the barriers stopping to be effective before the expiration of the options. Lastly we discuss the pricing formulas of the options whose barriers are not effective immediately but some time in the future within the life of the options .And the pricing formulas are worked out mainly via the approach of the reflection principle.At the same time , the innovation of this paper is to work out the three kinds of pricing formulas of barrier options of the geometric average assets .This paper takes down-out calls for example, as in most other situations, we can price all kinds of options as long as we know the distribution of the underlying asset price at maturity , so, we can price the down-in calls, up-out calls and so on by the same mean.