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

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Abstract

We introduce a class of interest rate models, called the \(\alpha\)-CIR model, which is a natural extension of the standard CIR model by adding a jump part driven by \(\alpha\)-stable Lévy processes with index \(\alpha\in(1,2]\). We deduce an explicit expression for the bond price by using the fact that the model belongs to the family of CBI and affine processes, and analyze the bond price and bond yield behaviors. The \(\alpha\)-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. Finally, we provide a thorough analysis of the jumps, and in particular the large jumps.

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Acknowledgements

We are grateful to Guillaume Bernis, Christa Cuchiero, Robert Dalang, Luca Di Persio, Zorana Grbac, Zenghu Li, Antonis Papapantoleon, Mathieu Rosenbaum, Wolfgang Runggaldier, Carlo Sgarra, Stefan Tappe, Nizar Touzi, and Wei Xu for interesting discussions and helpful comments. We also thank the two anonymous referees for providing insightful comments and suggestions. This work was partially supported by “Sino-French Research Program of Mathematics” and NSFC of China (11671216). We thank warmly BICMR Peking University for hospitality.

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Authors and Affiliations

  1. Institut de Science Financière et d’Assurances, Université Claude Bernard-Lyon 1, 50 Avenue Tony Garnier, 69007, Lyon, France

    Ying Jiao

  2. BICMR, Peking University, 100871, Beijing, China

    Ying Jiao

  3. School of Mathematical Sciences and LPMC, Nankai University, 300071, Tianjin, China

    Chunhua Ma

  4. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot-Paris 7, Site Sophie Germain, 75013, Paris, France

    Simone Scotti

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  1. Ying Jiao
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  2. Chunhua Ma
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  3. Simone Scotti
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Correspondence to Simone Scotti.

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Jiao, Y., Ma, C. & Scotti, S. Alpha-CIR model with branching processes in sovereign interest rate modeling. Finance Stoch 21, 789–813 (2017). https://doi.org/10.1007/s00780-017-0333-7

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  • DOI: https://doi.org/10.1007/s00780-017-0333-7

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