Multiple yield curve modelling with CBI processes

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See all articles by Claudio Fontana

Claudio Fontana

Université Paris VII Denis Diderot

Alessandro Gnoatto

University of Verona - Department of Economics

Guillaume Szulda

University Paris Diderot, Sorbonne Paris Cité

Date Written: November 7, 2019

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.
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

Fontana, Claudio and Gnoatto, Alessandro and Szulda, Guillaume, Multiple yield curve modelling with CBI processes (November 7, 2019). Available at SSRN: https://ssrn.com/abstract=

Claudio Fontana

Université Paris VII Denis Diderot ( email )

avenue de France
Paris, 75205
France

Alessandro Gnoatto (Contact Author)

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

Guillaume Szulda

University Paris Diderot, Sorbonne Paris Cité ( email )

Paris
France

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