  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.
