Positivity-preserving truncated Euler–Maruyama method for generalised Ait-Sahalia-type interest model

Deng, Shounian and Fei, Chen and Fei, Weiyin and Mao, Xuerong (2023) Positivity-preserving truncated Euler–Maruyama method for generalised Ait-Sahalia-type interest model. BIT Numerical Mathematics, 63 (4). 59. ISSN 0006-3835 (https://doi.org/10.1007/s10543-023-01000-x)

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Abstract

The well-known Ait-Sahalia-type interest model, arising in mathematical finance, has some typical features: polynomial drift that blows up at the origin, highly nonlinear diffusion, and positive solution. The known explicit numerical methods including truncated/tamed Euler–Maruyama (EM) applied to it do not preserve its positivity. The main interest of this work is to investigate the numerical conservation of positivity of the solution of generalised Ait-Sahalia-type model. By modifying the truncated EM method to generate positive sequences of numerical approximations, we obtain the rate of convergence of the numerical algorithm not only at time T but also over the time interval [0, T]. Numerical experiments confirm the theoretical results.

  • Item type:Article
    ID code:87135
    Dates:
    Date
    Event
    27 November 2023
    Published
    31 October 2023
    Accepted
    Notes:Copyright © 2023 Springer-Verlag. This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at https://doi.org/10.1007/s10543-023-01000-x.
    Subjects:Science > Mathematics
    Social Sciences > Finance
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:01 Nov 2023 16:57
    Last modified:09 Apr 2024 04:24
    URI:https://strathprints.strath.ac.uk/id/eprint/87135
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