Multiple Yield Curve Modelling with CBI Processes

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. We provide a complete analytical framework, including a detailed study of discounted exponential moments of CBI processes. The proposed framework yields explicit valuation formulae for all linear interest rate derivatives as well as 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.