Adaptive lattice methods for multi-asset models

Abstract

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 - Delta t, T] and the other performing one level of refinement for lambda% of a given time domain [0, T], where T is the time to maturity, At is the time step size and lambda > 0 is a constant. Numerical experiments are carried out for the European and American barder-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. (C) 2008 Elsevier Ltd. All rights reserved.