Optimising risk and return of non-maturing products by dynamic replication

The risk management of non-maturing products is an important issue for most banks, in particular for those with significant retail business. This task is complicated by the inherent options of the underlying products: Clients may add or withdraw volumes anytime, and the product rate can be adjusted by the bank as a matter of policy. Both properties make future cash flows uncertain. Usually non-maturing products are replicated by a portfolio of fix-maturity instruments. We show with real examples that popular approaches based on static investment or funding rules are inefficient. As an alternative we propose a novel method that we call "dynamic replication". Here frequently new decisions on the allocation of maturing tranches, corrected by volume changes, are made that are determined by a multistage stochastic optimisation model.

The approach described in this article is an improvement of an earlier model by Frauendorfer and Schürle (2007) with respect to some important details: Due to the curse of dimensionality, in the latter model decisions could be made only in yearly time steps. Now the number of stages can be extended to allow for monthly decisions. Furthermore, here a polyhedral risk measure is applied which is more appropriate for multistage applications than the shortfall optimization used in the previous paper. Finally, we apply advanced models for product rates and volumes as well as a scenario generation procedure that allows matching the observed kurtosis of interest rates better. The performance of the proposed method in comparison with traditional approaches is illustrated in a case study.