Author(s): TIE Zhangdepartmentofmathematics, SCHOOL Ofinformationscienceandengineering, NORTHEASTERN University, SHENYANG 110004, CHINA Shuhuazhangresearchcenterformathematicsandeconomics, TIANJIN Universityoffinanceandeconomics, TIANJIN 300222, CHINA Danmeizhudepartmentofmathematics, SCHOOL Ofinformationscienceandengineering, NORTHEASTERN University, SHENYANG 110004, china
Pages: 484-494
Year: 2009 Issue:  4
Journal: Journal of Computational Mathematics
Keyword:  American lookback options;  Finite difference approximation;  Stability and convergence;  Error estimates;
Abstract: <正> In this paper we are concerned with the pricing of lookback options with Americantype constrains. Based on the differential linear complementary formula associated withthe pricing problem, an implicit difference scheme is constructed and analyzed. We showthat there exists a unique difference solution which is unconditionally stable. Using thenotion of viscosity solutions, we also prove that the finite difference solution convergesuniformly to the viscosity solution of the continuous problem. Furthermore, by means ofthe variational inequality analysis method, the O(△t +△x~2)-order error estimate is derivedin the discrete L_2-norm provided that the continuous problem is sufficiently regular. Inaddition, a numerical example is provided to illustrate the theoretical results.