An Efficient Lattice Algorithm for the LIBOR Market Model

Abstract

Interest rate derivatives are a vitally important, and highly diverse, class of financial instruments. The LIBOR market model (LMM) framework greatly simplifies pricing the simpler types by modeling the forward rate at every maturity as being lognormal. But path-dependent payoffs, such as for a callable instrument or a range accrual note, introduce major problems. The workhorse for valuing such contracts in the equity space is the binomial or trinomial lattice. In this article, Xiao develops a pricing lattice within the LMM, with a grid-type architecture (rather than a tree), and shows that performance of the lattice-based model is orders of magnitude faster than Monte Carlo simulation.