Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay

Emmanuel Coffie; Xuerong Mao

doi:10.1016/j.cam.2020.113137

Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay

Emmanuel Coffie, Xuerong Mao

Mathematics And Statistics

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Abstract

The original Ait-Sahalia model of the spot interest rate proposed by Ait-Sahalia assumes constant volatility. As supported by several empirical studies, volatility is never constant in most financial markets. From application viewpoint, it is important we generalise the Ait-Sahalia model to incorporate volatility as a function of delay in the spot rate. In this paper, we study analytical properties for the true solution of this model and construct several new techniques of the truncated Euler-Maruyama (EM) method to study properties of the numerical solutions under the local Lipschitz condition plus Khasminskii-type condition. Finally, we justify that the truncated EM approximate solution can be used within a Monte Carlo scheme for numerical valuations of some financial instruments such as options and bonds.

Original language	English
Article number	113137
Journal	Journal of Computational and Applied Mathematics
Volume	383
Early online date	11 Aug 2020
DOIs	https://doi.org/10.1016/j.cam.2020.113137
Publication status	Published - 28 Feb 2021

Keywords

stochastic interest rate model
delay volatility
truncated EM scheme
strong convergence
Monte Carlo scheme

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10.1016/j.cam.2020.113137

Coffie-Mao-JCAM-2020-Truncated-Euler-Maruyama-method-for-generalised-Ait-Sahalia-type-interest-rateAccepted author manuscript, 352 KBLicence: CC BY-NC-ND 4.0

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title = "Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay",

abstract = "The original Ait-Sahalia model of the spot interest rate proposed by Ait-Sahalia assumes constant volatility. As supported by several empirical studies, volatility is never constant in most financial markets. From application viewpoint, it is important we generalise the Ait-Sahalia model to incorporate volatility as a function of delay in the spot rate. In this paper, we study analytical properties for the true solution of this model and construct several new techniques of the truncated Euler-Maruyama (EM) method to study properties of the numerical solutions under the local Lipschitz condition plus Khasminskii-type condition. Finally, we justify that the truncated EM approximate solution can be used within a Monte Carlo scheme for numerical valuations of some financial instruments such as options and bonds.",

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T1 - Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay

AU - Coffie, Emmanuel

AU - Mao, Xuerong

PY - 2021/2/28

Y1 - 2021/2/28

N2 - The original Ait-Sahalia model of the spot interest rate proposed by Ait-Sahalia assumes constant volatility. As supported by several empirical studies, volatility is never constant in most financial markets. From application viewpoint, it is important we generalise the Ait-Sahalia model to incorporate volatility as a function of delay in the spot rate. In this paper, we study analytical properties for the true solution of this model and construct several new techniques of the truncated Euler-Maruyama (EM) method to study properties of the numerical solutions under the local Lipschitz condition plus Khasminskii-type condition. Finally, we justify that the truncated EM approximate solution can be used within a Monte Carlo scheme for numerical valuations of some financial instruments such as options and bonds.

AB - The original Ait-Sahalia model of the spot interest rate proposed by Ait-Sahalia assumes constant volatility. As supported by several empirical studies, volatility is never constant in most financial markets. From application viewpoint, it is important we generalise the Ait-Sahalia model to incorporate volatility as a function of delay in the spot rate. In this paper, we study analytical properties for the true solution of this model and construct several new techniques of the truncated Euler-Maruyama (EM) method to study properties of the numerical solutions under the local Lipschitz condition plus Khasminskii-type condition. Finally, we justify that the truncated EM approximate solution can be used within a Monte Carlo scheme for numerical valuations of some financial instruments such as options and bonds.

KW - stochastic interest rate model

KW - delay volatility

KW - truncated EM scheme

KW - strong convergence

KW - Monte Carlo scheme

UR - https://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics

U2 - 10.1016/j.cam.2020.113137

DO - 10.1016/j.cam.2020.113137

M3 - Article

SN - 0377-0427

VL - 383

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 113137

ER -

Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay

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Keywords

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