Multiple Yield Curve Modelling With CBI Processes
29 Pages Posted: 18 Nov 2019
Date Written: November 7, 2019
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.
Keywords: Branching Process, Self-Exciting Process, Multi-Curve Model, Interest Rate, Libor Rate, OIS Rate, Multiplicative Spread, Affine Process
JEL Classification: E43, G12
Suggested Citation: Suggested Citation