A Spectral Algorithm for Pricing Interest Rate Options.

The paper describes a general spectral algorithm for numerical evaluation of contingent claims dependent on the term structure of interest rates. The evolution of the interest rates is modeled as a discrete Markov chain in a functional space. The functional basis in the state space and the transition probabilities of the Markov chain are naturally determined by the no-arbitrage condition. In the numerical implementation of the algorithm, computations are performed on a fixed grid of nodes; the numerical complexity of the algorithm is linear in the total number of the discretization nodes. The paper contains error estimates for the numerical procedure and convergence results. The algorithm is fast, consistent with other methods, and can be used for pricing a wide class of instruments. Citation Copyright 1996 by Kluwer Academic Publishers.