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.
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