Adaptive Binomial Tree Methods for Two-Asset Options

Adaptive binomial tree methods are developed to compute the price of exotic options with two underlying assets. A simple coordinate representation is used to extend one dimensional binomial method to multivariate asset models. Two algorithms are proposed, one performing several levels of refinements for t ∈[T-△t, T] and the other performing one level of refinement for λ% of a given domain [0, T], where T is the time to maturity, △t is the time step size and λ ＞ 0 is a constant. Both adaptive algorithms are numerically proven to improve efficiency over methods with uniform time step for a given level of accuracy.