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We present Monte Carlo-Euler methods for a weak approximation problem relatedto the Heath-Jarrow-Morton (HJM) term structure model, based on \Ito stochasticdifferential equations in infinite dimensional spaces, and prove strong andweak error convergence estimates. The weak error estimates are based onstochastic flows and discrete dual backward problems, and they can be used toidentify different error contributions arising from time and maturitydiscretization as well as the classical statistical error due to finitesampling. Explicit formulas for efficient computation of sharp errorapproximation are included. Due to the structure of the HJM models consideredhere, the computational effort devoted to the error estimates is low comparedto the work to compute Monte Carlo solutions to the HJM model. Numericalexamples with known exact solution are included in order to show the behaviorof the estimates.

Monte Carlo Euler approximations of HJM term structure financial models