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BIT Numerical Mathematics

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27-04-2019

On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case

Authors: Libo Li, Dai Taguchi

Published in: BIT Numerical Mathematics | Issue 3/2019

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Abstract

We propose a positivity preserving implicit Euler–Maruyama scheme for a jump-extended Cox–Ingersoll–Ross (CIR) process where the jumps are governed by a compensated spectrally positive \(\alpha \)-stable process for \(\alpha \in (1,2)\). Different to the existing positivity preserving numerical schemes for jump-extended CIR or constant elasticity variance process, the model considered here has infinite activity jumps. We calculate, in this specific model, the strong rate of convergence and give some numerical illustrations. Jump extended models of this type were initially studied in the context of branching processes and was recently introduced to the financial mathematics literature to model sovereign interest rates, power and energy markets.

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Title: On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case
Authors: Libo Li
Dai Taguchi
Publication date: 27-04-2019
Publisher: Springer Netherlands
Published in: BIT Numerical Mathematics / Issue 3/2019
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-019-00753-8

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