An efficient lattice Boltzmann model for the valuation of American multi-asset options

The valuation of American multi-asset options provides theoretical support for addressing complex financial problems, and is of significant importance in financial mathematics. The option pricing model can be formulated as an n -dimensional linear complementarity problem (LCP) on unbounded domains, for which an efficient numerical method is developed in this paper. First, to simplify computations, the LCP is converted into an unbounded nonlinear parabolic problem through variable replacement and the penalty method. Subsequently, for truncating the unbounded domain, the perfectly matched layer (PML) technique is employed. Finally, a lattice Boltzmann method (LBM) with second-order spatial accuracy is developed to solve the resulting model for pricing American basket put options on two underlying assets. Numerical simulations and comparisons with existing methods demonstrate the superiority of the present method for effectiveness and computational efficiency.