Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling

Ying Jiao, Chunhua Ma and Simone Scotti ()
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Ying Jiao: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Chunhua Ma: Nankai University, School of mathematical sciences - NKU - Nankai University
Simone Scotti: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique

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Abstract: We introduce a class of interest rate models, called the α-CIR model, which gives a natural extension of the standard CIR model by adopting the α-stable Lévy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rate together with the presence of large jumps at local extent. We emphasize on a general integral representation of the model by using random fields, with which we establish the link to the CBI processes and the affine models. Finally we analyze the jump behaviors and in particular the large jumps, and we provide numerical illustrations.

Date: 2017-06-01
Note: View the original document on HAL open archive server: https://hal.science/hal-01275397v2
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Published in Finance and Stochastics, 2017, 21 (3), pp.789-813

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