Multiple yield curve modelling with CBI processes

TL;DR

This paper introduces a new multi-curve interest rate model driven by CBI processes, capturing empirical spread features, contagion effects, and enabling explicit derivative valuation, with successful market calibration.

Contribution

It develops a parsimonious, tractable multi-curve model based on CBI processes, providing analytical valuation formulas and demonstrating market calibration.

Findings

Model reproduces empirical spread features

Enables explicit valuation of interest rate derivatives

Successfully calibrated to market data

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.