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

We introduce a class of interest rate models, called the alpha-CIR model, which gives a natural extension of the standard CIR model by adopting the alpha-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 emphasise 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 analyse the jump behaviours and in particular the large jumps, and we provide numerical illustrations.
This is a joint work with Ying Jiao and Chunhua Ma.