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

Shounian Deng; Chen Fei; Weiyin Fei; Xuerong Mao

doi:10.1016/j.physa.2019.122057

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

Shounian Deng, Chen Fei, Weiyin Fei, Xuerong Mao

Mathematics And Statistics

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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.

Original language	English
Article number	122057
Number of pages	18
Journal	Physica A: Statistical Mechanics and its Applications
Volume	533
Early online date	17 Jul 2019
DOIs	https://doi.org/10.1016/j.physa.2019.122057
Publication status	Published - 1 Nov 2019

Keywords

stochastic interest rate model
poisson jumps
EM method
convergence in probability

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Deng-etal-PhysicaA-2019-generalized-ait-sahalia-type-interest-rate-modelAccepted author manuscript, 830 KBLicence: CC BY-NC-ND 4.0

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

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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AU - Deng, Shounian

AU - Fei, Chen

AU - Fei, Weiyin

AU - Mao, Xuerong

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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.

AB - 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.

KW - stochastic interest rate model

KW - poisson jumps

KW - EM method

KW - convergence in probability

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DO - 10.1016/j.physa.2019.122057

M3 - Article

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VL - 533

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 122057

ER -

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

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Keywords

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