Primal Dual Active Set Method For Solving Basket Options Pricing Problem

In this thesis,we focus on American basket option pricing problem,systematically analyze the essential di culties of numerically solving this problem,and give an effective numerical algorithm,which is called the primal dual active set algorithm.Based on the BlackScholes(B-S)model,we first analyze the American multi-asset option in general case.This model is a multi-dimensional variable coe cient backward parabolic model,which satisfies the linear complementarity problem.We take the basket option as an example.Through the standard transformations and far field truncation method,the B-S model is transformed into a multi-dimensional constant coe cient forward parabolic problem on a bounded domain.Then the corresponding variational formulation is given,and the numerical scheme is designed based on finite element discretization.Furthermore,the primal dual active set method is used to solve the discretized system,where the numerical solution and the optional exercise boundary are obtained simultaneously.Finally,numerical experiments are shown to verify the accuracy and e ciency of our method.