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Modelling interest rates by correlated multi-factor CIR-like processes

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  • L. Bertini
  • L. Passalacqua

Abstract

We investigate the joint description of the interest-rate term stuctures of Italy and an AAA-rated European country by mean of a --here proposed-- correlated CIR-like bivariate model where one of the state variables is interpreted as a benchmark risk-free rate and the other as a credit spread. The model is constructed by requiring the strict positivity of interest rates and the asymptotic decoupling of the joint distribution of the two state variables on a long time horizon. The second condition is met by imposing the reversibility of the process with respect to a product measure, the first is then implemented by using the tools of potential theory. It turns out that these conditions select a class of non-affine models, out of which we choose one that is quadratic in the two state variables both in the drift and diffusion matrix. We perform a numerical analysis of the model by investigating a cross section of the term structures comparing the results with those obtained with an uncoupled bivariate CIR model.

Suggested Citation

  • L. Bertini & L. Passalacqua, 2008. "Modelling interest rates by correlated multi-factor CIR-like processes," Papers 0807.3898, arXiv.org.
    • Handle: RePEc:arx:papers:0807.3898
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    File URL: http://arxiv.org/pdf/0807.3898
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    Cited by:

    1. Duc, Luu Hoang & Tran, Tat Dat & Jost, Jürgen, 2018. "Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3253-3272.
    2. Gerald H. L. Cheang & Len Patrick Dominic M. Garces, 2020. "Representation of Exchange Option Prices under Stochastic Volatility Jump-Diffusion Dynamics," Papers 2002.10202, arXiv.org.

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