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

Efficient simulation and calibration of general HJM models by splitting schemes