# 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.
Original language English 122057 18 Physica A: Statistical Mechanics and its Applications 533 17 Jul 2019 https://doi.org/10.1016/j.physa.2019.122057 Published - 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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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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author = "Shounian Deng and Chen Fei and Weiyin Fei and Xuerong Mao",
year = "2019",
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language = "English",
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journal = "Physica A: Statistical Mechanics and its Applications",
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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

TY - JOUR

T1 - Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation

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

U2 - 10.1016/j.physa.2019.122057

DO - 10.1016/j.physa.2019.122057

M3 - Article

VL - 533

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

M1 - 122057

ER -