Spectral Method for the Black-Scholes Model of American Options Valuation  

作　　者：Haiming Song Ran Zhang WenYi Tian 

机构地区：[1]Department of Mathematics,Jilin University,Changchun,130012,P.R.China [2]Department of Mathematics,Hong Kong Baptist University,Hong Kong

出　　处：《Journal of Mathematical Study》2014年第1期47-64,共18页数学研究（英文）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.11271157,11371171);the Open Project Programof the State Key Lab of CAD&CG(A1302)of Zhejiang University and the Scientific Research Foundation for Returned Scholars,Ministry of Education of China.

摘　　要：In this paper,we devote ourselves to the research of numerical methods for American option pricing problems under the Black-Scholes model.The optimal exercise boundary which satisfies a nonlinear Volterra integral equation is resolved by a high-order collocationmethod based on gradedmeshes.For the other spatial domain boundary,an artificial boundary condition is applied to the pricing problem for the effective truncation of the semi-infinite domain.Then,the front-fixing and stretching transformations are employed to change the truncated problemin an irregular domain into a one-dimensional parabolic problem in[−1,1].The Chebyshev spectral method coupledwith fourth-order Runge-Kuttamethod is proposed for the resulting parabolic problem related to the options.The stability of the semi-discrete numerical method is established for the parabolic problemtransformed fromthe originalmodel.Numerical experiments are conducted to verify the performance of the proposed methods and compare them with some existing methods.

关 键 词：American option pricing Black-Scholes model optimal exercise boundary frontfixing Chebyshev spectral method Runge-Kutta method 

分 类 号：O17[理学—数学]