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On non-negative modeling with CARMA processes

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Two stationary and non-negative processes that are based on continuous-time autoregressive moving average (CARMA) processes are discussed. First, we consider a generalization of Cox–Ingersoll–Ross (CIR) processes. Next, we consider CARMA processes driven by compound Poisson processes with exponential jumps which are generalizations of Ornstein–Uhlenbeck (OU) processes driven by the same noise. The way in which the two processes generalize CIR and OU processes and the relation between them will be discussed. Furthermore, the stationary distribution, the autocorrelation function, and pricing of zero-coupon bonds are considered.

Original languageEnglish
JournalJournal of Mathematical Analysis and Applications
Volume476
Issue1
Pages (from-to)196-214
Number of pages19
ISSN0022-247X
DOIs
Publication statusPublished - 2019

    Research areas

  • Continuous-time ARMA processes, Lévy processes, Ornstein–Uhlenbeck processes, Square-root process, Stationary processes

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