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Monte-Carlo simulation results in estimating a pure-jump Cox-Ingersoll-Ross process.

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Title: Monte-Carlo simulation results in estimating a pure-jump Cox-Ingersoll-Ross process.
Authors: Bayraktar, Elise (AUTHOR) elise.bayraktar@univ-eiffel.fr
Source: ESAIM: Proceedings & Surveys. 2025, Vol. 79, p2-16. 15p.
Subjects: Jump processes, Lévy processes, Monte Carlo method, Scientific observation, Simulation methods & models, Stochastic processes, Parameter estimation, Statistical accuracy
Abstract (English): 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 [BC23]. 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. [ABSTRACT FROM AUTHOR]
Abstract (French): Nous considérons un processus de Cox-Ingersoll-Ross stable (α-stable CIR) dirigé par un processus de Lévy stable non symétrique d'indice d'activité des sauts α ∈ (1,2), pour lequel des estimateurs des paramètres de tendance, d'échelle et d'activité des sauts à partir d'observations haute fréquence du processus sur une période de temps fixe ont été proposés dans des travaux antérieurs [BC23]. Nous présentons d'abord un schéma numérique pour simuler ce processus. Ensuite, nous décrivons la difficulté que représente le processus de Lévy stable non symétrique lors du calcul de sa densité et de ses dérivées. Enfin, nous implémentons les estimateurs et effectuons des simulations de Monte-Carlo pour montrer la bonne précision de l'estimation. [ABSTRACT FROM AUTHOR]
Copyright of ESAIM: Proceedings & Surveys is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Monte-Carlo simulation results in estimating a pure-jump Cox-Ingersoll-Ross process.
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  Data: <searchLink fieldCode="AR" term="%22Bayraktar%2C+Elise%22">Bayraktar, Elise</searchLink> (AUTHOR)<i> elise.bayraktar@univ-eiffel.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22ESAIM%3A+Proceedings+%26+Surveys%22">ESAIM: Proceedings & Surveys</searchLink>. 2025, Vol. 79, p2-16. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Jump+processes%22">Jump processes</searchLink><br /><searchLink fieldCode="DE" term="%22Lévy+processes%22">Lévy processes</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+observation%22">Scientific observation</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Parameter+estimation%22">Parameter estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+accuracy%22">Statistical accuracy</searchLink>
– Name: Abstract
  Label: Abstract (English)
  Group: Ab
  Data: 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 [BC23]. 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. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label: Abstract (French)
  Group: Ab
  Data: Nous considérons un processus de Cox-Ingersoll-Ross stable (α-stable CIR) dirigé par un processus de Lévy stable non symétrique d'indice d'activité des sauts α ∈ (1,2), pour lequel des estimateurs des paramètres de tendance, d'échelle et d'activité des sauts à partir d'observations haute fréquence du processus sur une période de temps fixe ont été proposés dans des travaux antérieurs [BC23]. Nous présentons d'abord un schéma numérique pour simuler ce processus. Ensuite, nous décrivons la difficulté que représente le processus de Lévy stable non symétrique lors du calcul de sa densité et de ses dérivées. Enfin, nous implémentons les estimateurs et effectuons des simulations de Monte-Carlo pour montrer la bonne précision de l'estimation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of ESAIM: Proceedings & Surveys is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1051/proc/202579002
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        Text: English
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        PageCount: 15
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      – SubjectFull: Jump processes
        Type: general
      – SubjectFull: Lévy processes
        Type: general
      – SubjectFull: Monte Carlo method
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      – SubjectFull: Scientific observation
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      – SubjectFull: Simulation methods & models
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      – SubjectFull: Stochastic processes
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      – SubjectFull: Parameter estimation
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      – SubjectFull: Statistical accuracy
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      – TitleFull: Monte-Carlo simulation results in estimating a pure-jump Cox-Ingersoll-Ross process.
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              Text: 2025
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