2. Short-Rate and Rational Pricing Kernel Models for Multiple Curves

In this chapter we consider mainly strict-sense short-rate models in view of constructing multiple curves. Because the pre-crisis rational pricing kernel models can be seen as short-rate models in a wider sense, we shall furthermore present some recent multi-curve extensions of these models as well. For the strict-sense short rate models we consider a basic OIS short rate and various spreads to be added on top of it, one for each of the multiple curves. The setup is mainly that of exponentially affine, but also exponentially quadratic models driven by several stochastic factors. This allows us to obtain explicit formulas for various linear and optional interest rate derivatives also in the multi-curve setting.