Parsimonious HJM modelling for multiple yield curve dynamics

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Notes

The opinions here expressed are solely those of the authors and do not represent in any way those of their employers.

See European Banking Federation site at http://www.euribor-ebf.eu.

See for instance Eisenschimdt and Tapking (2009) where the Euribor-Eurepo spread is used as an indicator of credit risk.

See appendix A for vector and matrix notation.

For instance day.

This assumption may be generalized asking that for a function such that when .

Actually, starting from (6), and switching to the terminal measure, we have

The swap rate is a martingale under the swap measure, since it is the ratio of a tradable asset over the swap annuity, which, in turn, is the numeraire of the swap measure. See, for instance, Brigo and Mercurio (2006). Thus, we have zero drift, and we do not need to calculate explicitly the drift of forward Libor rates under swap measure.

See for instance Pallavicini and Tarenghi (2010) for a seminal empirical analysis.

As the are deterministic, this model is often written by explicitly computing the -related quantities such as the drift of the Those quantities are then incorporated into a generic shift.