Wiener chaos expansion and numerical solutions of the Heath–Jarrow–Morton interest rate model

Nikolaos Thomaidis, Evangelia A. Kalpinelli and Athanasios N. Yannacopoulos

Abstract

ABSTRACT

In this paper, we propose and analyze a simple and fast numerical method for the solution of the stochastic Heath-Jarrow-Morton (HJM) interest rate model under the Musiela parameterization, based on theWiener chaos expansion (WCE). Through the proposed method, the infinite-dimensional HJM equation is approximated by a finite system of partial differential equations (PDEs), which can be addressed by standard techniques. To illustrate the general construction, we approximate the value of the US treasury bond in an HJM framework, and the results are compared with those derived by the Monte Carlo method and the ensemble Kalman filter. The proposed method is computationally efficient compared with the standard techniques, and it provides a convenient way to compute the statistical moments of the solution numerically. Numerical results and useful formulas for estimating the stochastic duration and immunization are presented.