美式多资产期权定价问题的格子Boltzmann方法  

Lattice Boltzmann Method for Pricing American Multi-asset Options

作　　者：李聪 武芳芳[1] LI Cong;WU Fangfang(School of Science,Shenyang University of Technology,Shenyang 110870,China)

机构地区：[1]沈阳工业大学理学院,沈阳110870

出　　处：《湖北民族大学学报（自然科学版）》2022年第3期350-355,共6页Journal of Hubei Minzu University:Natural Science Edition

基　　金：国家自然科学基金项目(62103289);辽宁省科学技术计划项目(2019-ZD-0209)。

摘　　要：利用格子Boltzmann方法求解美式多资产期权定价问题.首先利用惩罚法将描述美式多资产期权定价问题的线性互补模型化为抛物问题,并采用远场截断法将求解区域有界化;然后针对转化后的模型,进行多尺度Chapman-Enskog展开,选取恰当平衡态分布函数和补偿函数,分别恢复出具有二阶精度和三阶精度的宏观方程;最后进行数值模拟.结果表明本文得到的期权价格与现有数值方法得到期权价格的图像相吻合,验证了所建模型的有效性,该模型的建立为求解更多期权定价问题提供了参考.Lattice Boltzmann method is used to solve the pricing problem of American multi-asset options.Firstly,the penalty function method is used to transform the linear complementary model of the pricing problem of American multi-asset options into a nonlinear parabolic problem,and the far field estimate method is used to bound the solution region.Secondly,the Chapman-Enskog expansion is performed for the transformed model,and the appropriate equilibrium state distribution function and the compensation function are selected to restore the macroscopic equations with the second order accuracy and the third order accuracy.Finally,the numerical simulation results show that the images of option prices obtained by lattice Boltzmann model agree well with the others obtained by the existing numerical methods,which verify the effectiveness of the proposed algorithm.Lattice Boltzmann model can also be generalized to price more options.

关 键 词：格子BOLTZMANN方法 美式多资产期权 惩罚法 远场截断法 

分 类 号：O241.82[理学—计算数学]