美式回望期权定价问题的格子Boltzmann模型求解

doi:10.13438/j.cnki.jdzk.2025.02.003

摘要/Abstract

摘要：用格子Boltzmann模型（LBM）求解美式回望看跌期权定价问题.利用区域截断技巧和惩罚法，将回望期权满足的线性互补问题转化为有界区域上的一维非线性抛物问题，并对转化后的方程引入LBM，选取恰当的平衡态分布函数和修正函数恢复出宏观方程.数值模拟结果表明，LBM获得的期权价格与二叉树法等得到的结果吻合较好，验证了该模型求解美式回望期权定价问题的有效性.

关键词： 格子Boltzmann模型, 美式回望期权, 线性互补问题, 区域截断技巧, 惩罚法

Abstract: The lattice Boltzmann model (LBM) is used to solve the pricing problem of the American lookback option.The domain truncation technique and the penalty method are used to transform the linear complementary model satisfied by the lookback option into a one-dimensional nonlinear parabolic problem on a bounded domain,and LBM is introduced for the transformed bounded domain problem.The macroscopic equation is recovered by selecting appropriate equilibrium distribution functions and amending functions.The numerical simulation results show that the option prices obtained by LBM agree well with the results derived from the binomial tree method and other methods,which verify the effectiveness of the model in solving the pricing problem of the American lookback option.

Key words: lattice Boltzmann model, American lookback option, linear complementarity problem, domain truncation technique, penalty method

张艺, 武芳芳, 张琪. 美式回望期权定价问题的格子Boltzmann模型求解[J]. 吉首大学学报（自然科学版）, 2025, 46(2): 23-30.

ZHANG Yi, WU Fangfang, ZHANG Qi. Lattice Boltzmann Model for Pricing American Lookback Option[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(2): 23-30.

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