Multiple yield curve modelling with CBI processes

Claudio Fontana, Alessandro Gnoatto and Guillaume Szulda

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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.

Date: 2019-11, Revised 2020-10
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1911.02906

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