Monte-Carlo simulation results in estimating a pure-jump Cox-Ingersoll-Ross process
Résumé
We consider a pure-jump stable Cox-Ingersoll-Ross (α-stable CIR) process driven by a non-symmetric stable Lévy process with jump activity α ∈ (1, 2), for which estimators of the drift, scaling and jump activity parameters from high-frequency observations of the process on a fixed time period have been proposed in previous work. We first present a numerical scheme to simulate this process. Next, we describe the challenge presented by the non-symmetric stable Lévy process when computing its density and its derivatives. We finally implement the estimators and carry out simulations to show good estimation accuracy.
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