Multiple yield curve modelling with CBI processes
29 Pages Posted:
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
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