Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation

Shounian Deng, Chen Fei, Weiyin Fei, Xuerong Mao

Research output: Contribution to journalArticle

Abstract

In this paper, we consider a generalized Ait-Sahalia interest rate model with Poisson jumps in finance. The analytical properties including positivity, boundedness and pathwise asymptotic estimations of the solution to this model are investigated. Moreover, we prove that the EulerMaruyama (EM) numerical solution converges to the true solution of the model in probability. Finally, we apply the EM solution to compute some financial quantities. A numerical example is provided to demonstrate the effectiveness of our results.
LanguageEnglish
Article number122057
Number of pages18
JournalPhysica A: Statistical Mechanics and its Applications
Volume533
Early online date17 Jul 2019
DOIs
Publication statusPublished - 1 Nov 2019

Fingerprint

Interest Rate Models
Numerical Approximation
Siméon Denis Poisson
Jump
approximation
Finance
Positivity
finance
Boundedness
Numerical Solution
Converge
Numerical Examples
Model
Demonstrate

Keywords

  • stochastic interest rate model
  • poisson jumps
  • EM method
  • convergence in probability

Cite this

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abstract = "In this paper, we consider a generalized Ait-Sahalia interest rate model with Poisson jumps in finance. The analytical properties including positivity, boundedness and pathwise asymptotic estimations of the solution to this model are investigated. Moreover, we prove that the EulerMaruyama (EM) numerical solution converges to the true solution of the model in probability. Finally, we apply the EM solution to compute some financial quantities. A numerical example is provided to demonstrate the effectiveness of our results.",
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Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation. / Deng, Shounian; Fei, Chen; Fei, Weiyin; Mao, Xuerong.

In: Physica A: Statistical Mechanics and its Applications, Vol. 533, 122057, 01.11.2019.

Research output: Contribution to journalArticle

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KW - convergence in probability

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