  We develop a modelling framework for multiple yield curves driven by
continuous-state branching processes with immigration (CBI processes).
Exploiting the self-exciting behavior of CBI jump processes, this approach can
reproduce the relevant empirical features of spreads between different
interbank rates. In particular, we introduce multi-curve models driven by a
flow of tempered alpha-stable CBI processes. Such models are especially
parsimonious and tractable, and can generate contagion effects among different
spreads. We provide a complete analytical framework, including a detailed study
of discounted exponential moments of CBI processes. The proposed approach
allows for explicit valuation formulae for all linear interest rate derivatives
and semi-closed formulae for non-linear derivatives via Fourier techniques and
quantization. We show that a simple specification of the model can be
successfully calibrated to market data.
