  We introduce efficient numerical methods for generic HJM equations of
interest rate theory by means of high-order weak approximation schemes. These
schemes allow for QMC implementations due to the relatively low dimensional
integration space. The complexity of the resulting algorithm is considerably
lower than the complexity of multi-level MC algorithms as long as the optimal
order of QMC-convergence is guaranteed. In order to make the methods applicable
to real world problems, we introduce and use the setting of weighted function
spaces, such that unbounded payoffs and unbounded characteristics of the
equations in question are still allowed. We also provide an implementation,
where we efficiently calibrate an HJM equation to caplet data.
