Multiple yield curve modelling with CBI processes (Q2037767)

The authors develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). The flow of CBI processes is a family of processes \(\{Y_i;i=1,\ldots,m\}\) which have a common branching mechanism, share the same volatility coefficients, the same jump measure and the same speed of mean-reversion. Such models are especially parsimonious and tractable, and can generate contagion effects among different spreads.\newline In particular, the authors introduce multi-curve models driven by a flow of tempered alpha-stable CBI processes and provide a complete analytical framework, including a detailed study of discounted exponential moments of CBI processes. \newline 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. It is shown that a simple specification of the model can be successfully calibrated to market data.