Numerical Methods For Barrier Option Pricing

In this paper,we propose finite element method(FEM)for solving the Barrier options pricing problems.Barrier option is a weak path-related option,and it is well known that the Barrier options has many applications.But most of Barrier options are difficult to obtain analytical solutions.Here,we only consider the call double knock-out Barrier option as an example.Based on Black-Scholes model,we deduce the parabolic problem model for the Barrier option,which is a backward variable coefficient parabolic problem on the irregular region.For solving such problems,we first transform it into a positive parabolic partially differential equations with constant coefficients on the irregular area.Then,we transform the irregular region into a rule region,use the FEM to solve the problem,and derive the corresponding error analysis.Finally,The option price's numerical approximations obtained by a series of inverse transformation.Numerical experiments verify the efficiency of our methods.