Pricing Double Exponential Barriers Chained Option

Barrier options, because of its flexibility and compared with the ordinary option has the advantage of low price, is widely used as a kind of path dependent derivatives. Usually assume that the lower or upper barrier of barrier options(unilateral or bilateral border barriers) is constant, but this is a simplified the ideal state. While the barrier in reality is often curve which is changed and the logarithmic of curve(or index) barrier is a linear function of time. The barrier option is monitored at random time, that is when the underlying asset price exceeds a certain level for the first time. When we assume that the index boundary is the theoretical premise, discuss the the case that the index barrier according to a specified order through the two or more barriers. Power option is a variation of option that changing the structure of option. But because of the structure variation of power option,it is possible to achieve great leverage.The option price will change a lot, when underlying asset price slightly raise a little, which gives speculators the opportunity to manipulate the market.While the power barrier option is the exotic option to avoid arbitrage. This article is to be considered complete, continuous market model, underlying asset price follows a geometric Brownian motion. Using Girsanov theorem, the reflection principle and other methods, the article is discussed in a specified order given in a simple index chained power barrier options under the option pricing problem, we give a double exponential barrier chain exact power option pricing formula, and gives a simple numerical examples.