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

Libo Li, Dai Taguchi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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 α-stable process for α∈ (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.

Original languageEnglish
Pages (from-to)747-774
Number of pages28
JournalBIT Numerical Mathematics
Volume59
Issue number3
DOIs
Publication statusPublished - Sep 1 2019

Keywords

  • Alpha-CIR models
  • Euler–Maruyama scheme
  • Hölder continuous coefficients
  • Implicit scheme
  • Lévy driven SDEs
  • Spectrally positive Lévy process

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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