A lattice method for option pricing with two underlying assets in the regime-switching model

In this work we develop an efficient lattice approach for option pricing with two underlying assets whose prices are governed by regime-switching models. Jump amplitudes are specified in a way such that the lattice achieves complete node recombination along each asset variable and grows quadratically as the number of time steps increases. Jump probabilities are obtained by solving a related quadratic programming problem. The weak convergence of the discrete lattice approximations to the continuous-time regime-switching diffusion processes is established. The lattice is employed to price both European and American options written on the maximum and minimum of two assets in different regimes. Numerical results are provided and compared for the European options with a Monte-Carlo simulation approach.