Adaptive lattice methods for multi-asset models

Adaptive lattice methods are developed to compute the price of multivariate contingent claims. A simple coordinate representation is used to extend one dimensional lattice methods to multivariate asset models. Two algorithms are proposed, one performing several levels of refinement for a time interval [T−Δt,T] and the other performing one level of refinement for λ%λ% of a given time domain [0,T][0,T], where TT is the time to maturity, Δt is the time step size and λ>0λ>0 is a constant. Numerical experiments are carried out for the European and American barrier-type options with one, two, or three underlying assets. In our numerical experiments, both adaptive algorithms improve efficiency over lattice methods with a uniform time step for the same level of accuracy.