Pricing Barrier Options For Lévy Process With Fuzzy Parameters

Barrier option is one of the new options, which is path-dependent. Its payment depends on whether the price of underlying asset can reach to a pointed barrier level. First, the barrier options can guard against the risk and speculation and avoid huge losses of possible market spike, which also can maintain continuity and stability of operations; second, the premium of barrier options is low. A large number of investors pay attention to barrier option because of its characters.There is much study on barrier option pricing. The usual pricing study is the underlying assets price which follows geometrical Brownian motion. Geometrical Brownian motion can't describe jumps of underlying assets price caused by external shocks (such as earthquakes, tsunami). This paper uses geometrical Levy process as basic model studying option pricing in order to describe jumps of underlying assets price.This paper borrowed the idea of Piotr Nowak and Maciej Romaniuk who gave the pri-cing formula at time 0 of European options in the case of underlying asset price following geometrical Levy process. We deduced the pricing formula at time t of European options and Barrier options. Because many of the parameters in the model are not be determined precisely, these parameters may be expressed as fuzzy numbers. We can get the pricing formula of Barrier options in fuzzy case.We simulate the price tracks of the underlying asset by Monte Carlo method to obtain the numerical simulation results using Matlab. We use the fuzzy numbers and Mathematica to calculate the price interval of the option.