Journal ArticleDOI
Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling
TLDR
The α-CIR model as mentioned in this paper is an extension of the standard CIR model by adopting the α-stable Levy process and preserving the branching property, which allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market together with the presence of large jumps at local extent.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 Levy 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.read more
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Book ChapterDOI
Continuous-State Branching Processes with Immigration
TL;DR: In this paper, a brief introduction to continuous-state branching processes with or without immigration is given, where the processes are constructed by taking rescaling limits of classical discrete state branching models and given characterizations of the local and global maximal jumps of the processes.
Journal ArticleDOI
A branching process approach to power markets
TL;DR: A market model for power prices is investigated, including most basic features exhibited by previous models and taking into account self-exciting properties, and a Random Field approach is proposed, extending Hawkes-type models by introducing a twofold integral representation property.
Journal ArticleDOI
The Alpha-Heston stochastic volatility model
TL;DR: In this paper, an affine extension of the Heston model is introduced where the instantaneous variance process contains a jump part driven by α-stable processes with α ∆ in(1,2]$ in(α ∆)-stable processes.
Journal ArticleDOI
Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations
TL;DR: In this paper, the authors consider a stable Cox-Ingersoll-Ross process driven by a standard Wiener process and a spectrally positive strictly stable Levy process, and study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations.
Journal ArticleDOI
On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case
Libo Li,Dai Taguchi +1 more
TL;DR: In this paper, a positivity preserving implicit Euler-Maruyama scheme for a jump-extended Cox-Ingersoll-Ross (CIR) process with infinite activity jumps is proposed.
References
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Journal ArticleDOI
Spectra of some self-exciting and mutually exciting point processes
TL;DR: In this paper, the theoretical properties of a class of processes with particular reference to the point spectrum or corresponding covariance density functions are discussed and a particular result is a self-exciting process with the same second-order properties as a certain doubly stochastic process.