Numerical integration of Heath-Jarrow-Morton model of interest rates

Abstract: We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic differential equations (SDEs) which we approximate in the weak and mean-square sense using the general theory of numerical integration of SDEs. The proposed numerical algorithms are computationally highly efficient due to the use of high-order quadrature rules which allow us to take relatively large discretization steps in the maturity time without affecting overall accuracy of the algorithms. Convergence theorems for the methods are proved. Results of some numerical experiments with European-type interest rate derivatives are presented.