Multiple yield curve modelling with CBI processes
Abstract
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.
Cite
@article{arxiv.1911.02906,
title = {Multiple yield curve modelling with CBI processes},
author = {Claudio Fontana and Alessandro Gnoatto and Guillaume Szulda},
journal= {arXiv preprint arXiv:1911.02906},
year = {2020}
}