Work

Lattice Boltzmann method with a PML technique for pricing American lookback put options

Year: 2025

Type: article

Abstract: This paper proposes an efficient lattice Boltzmann method (LBM) with the perfectly matched layer (PML) technique for pricing American lookback put options. The pricing model for American lookback put options is formulated as a two-dimensional linear complementarity problem (LCP) on an unbounded domain. First, by using variable substitution and the penalty method, the LCP is transformed into a one-dimensional unbounded parabolic problem. To address the unbounded domain, a PML technique is introduced to truncate it. Subsequently, an effective lattice Boltzmann model is developed to solve the resulting bounded nonlinear parabolic problem. By selecting the appropriate equilibrium distribution functions and amending functions, the macroscopic equation is recovered. Finally, several numerical simulations are conducted to validate the efficiency of the proposed method.

Source: Communications in Nonlinear Science and Numerical Simulation

DOI: 10.1016/j.cnsns.2025.109149

Authors: Fangfang Wu, Shuangyi Wang, Xiaoxiao Dong, Ming Tian

Institution: Shenyang University of Technology

Language: English

Topic: Lattice Boltzmann Simulation Studies

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,710

Funders: Natural Science Foundation of Liaoning Province, Department of Education of Liaoning Province