Multiple yield curve modelling with CBI processes

@article{Fontana2019MultipleYC,
  title={Multiple yield curve modelling with CBI processes},
  author={Claudio Fontana and Alessandro Gnoatto and Guillaume Szulda},
  journal={Mathematics and Financial Economics},
  year={2019},
  pages={1-32}
}
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… 

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References

SHOWING 1-10 OF 54 REFERENCES

Affine multiple yield curve models

We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or Heath–Jarrow–Morton modeling, can

A self‐exciting modeling framework for forward prices in power markets

This work proposes and investigates two model classes for forward power price dynamics, based on continuous branching processes with immigration, and on Hawkes processes with exponential kernel, respectively, and presents the conclusions about the adequacy of these models in describing the forward prices evolution.

The Multi-Curve Potential Model

We develop a general class of multi-curve potential models for post-crisis interest rates. Our model features positive stochastic basis spreads, positive term structures, and analytic pricing

Multiple curve Lévy forward price model allowing for negative interest rates

In this paper, we develop a framework for discretely compounding interest rates that is based on the forward price process approach. This approach has a number of advantages, in particular in the

Alpha-CIR model with branching processes in sovereign interest rate modeling

The α$\alpha$-CIR model allows us to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rates together with the presence of large jumps.

Looking Forward to Backward-Looking Rates: A Modeling Framework for Term Rates Replacing LIBOR

In this paper, we define and model forward risk-free term rates, which appear in the payoff definition of derivatives, and possibly cash instruments, based on the new interest-rate benchmarks that

LIBOR Market Model with Stochastic Basis

The post-credit crunch period has been characterized by non-negligible basis spreads between various rates that previously used to closely track each other. This has resulted into a shift from the

Quantization meets Fourier: a new technology for pricing options

  • Annals of Operations Research
  • 2018

INTERBANK CREDIT RISK MODELING WITH SELF-EXCITING JUMP PROCESSES

The credit crunch of 2007 caused major changes in the market of interbank rates making the existing interest rate theory inconsistent. This paper puts forward one way to reconcile practice and theory
...