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

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.