  The recent financial crisis has led to so-called multi-curve models for the
term structure. Here we study a multi-curve extension of short rate models
where, in addition to the short rate itself, we introduce short rate spreads.
In particular, we consider a Gaussian factor model where the short rate and the
spreads are second order polynomials of Gaussian factor processes. This leads
to an exponentially quadratic model class that is less well known than the
exponentially affine class. In the latter class the factors enter linearly and
for positivity one considers square root factor processes. While the square
root factors in the affine class have more involved distributions, in the
quadratic class the factors remain Gaussian and this leads to various
advantages, in particular for derivative pricing. After some preliminaries on
martingale modeling in the multi-curve setup, we concentrate on pricing of
linear and optional derivatives. For linear derivatives, we exhibit an
adjustment factor that allows one to pass from pre-crisis single curve values
to the corresponding post-crisis multi-curve values.
