Abstract
In this paper, a lattice Boltzmann method is proposed for solving the linear complementarity problem (LCP) arising in single and multi-asset American put option pricing. The LCP for American option is a variable coefficient parabolic model defined on an unbounded domain. Initially, using the far field estimate method and the penalty method respectively, the LCP could be reformulated into a nonlinear parabolic partial differential equation on a bounded domain. To construct a unified lattice Boltzmann model for the option pricing problems, the above transformation equations are rewritten into an equivalent divergence form. Then, through the incorporation of an amending function into the evolution equation, which assists in recovering the source term and eliminating the error term, the lattice Boltzmann model with spatial second-order accuracy is constructed. Finally, the present model is validated using numerical simulations, and the numerical results agree well with the option values obtained by existing methods, which indicates that the present lattice Boltzmann model is efficient for solving the American put option pricing problem.
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